Answer:
p(at most one space between) = (4n-6)/(n(n-1))
Step-by-step explanation:
There are n-1 ways the cars can be parked next to each other, and n-2 ways they can be parked with one empty space between. So, the total number of ways the cars can be parked with at most one empty space is ...
(n -1) +(n -2) = 2n-3
The number of ways that 2 cars can be parked in n spaces is ...
(n)(n -1)/2
So, the probability is ...
(2n-3)/((n(n-1)/2) = (4n -6)/(n(n -1))
___
If the cars are considered distinguishable and order matters, then the number of ways they can be parked will double. The factor of 2 cancels in the final probability ratio, so the answer remains the same.
__
Check
For n=2 or 3, p=1 as you expect.
For n=4, p=5/6, since there is only one of the 6 ways the cars can be parked that has 2 spaces between.
The probability that there is at most one empty parking space between Mary and Tom's cars is (2n - 3) / n.
We have,
To find the probability that there is at most one empty parking space between Mary and Tom's cars, we need to consider two scenarios:
Mary and Tom park their cars in adjacent spaces.
Mary and Tom park their cars in spaces with one empty space in between them.
Scenario 1: Mary and Tom park their cars in adjacent spaces.
In this case, there are (n - 1) ways for them to pick adjacent spaces out of the n spaces. Since there are n spaces to choose from initially, the probability for this scenario is (n - 1) / n.
Scenario 2: Mary and Tom park their cars with one empty space between them.
In this case, there are (n - 2) ways to pick two parking spaces with one empty space in between them. Again, since there are n spaces to choose from initially, the probability for this scenario is (n - 2) / n.
Now, we add up the probabilities of both scenarios because they are mutually exclusive:
Total Probability = Probability of Scenario 1 + Probability of Scenario 2
Total Probability = [(n - 1) / n] + [(n - 2) / n]
To make these fractions have a common denominator, we can rewrite them as:
Total Probability = [(n - 1) + (n - 2)] / n
Total Probability = [2n - 3] / n
Thus,
The probability that there is at most one empty parking space between Mary and Tom's cars is (2n - 3) / n.
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Britney is going to the candy store to buy 20 pieces of candy. She is going to buy chocolate candy and caramel candy. Each piece of chocolate candy costs 50 cents, and each piece of caramel candy costs 10 cents. You know that Britney spent $6.80 and bought 20 pieces of candy. She bought ______ pieces of chocolate.
A sample of n = 9 college students is used to evaluate the effectiveness of a new Study Skills Workshop. Each student’s grade point average (GPA) is recorded for the semester before the workshop and for the semester after the workshop. The average GPA improved by MD = 0.60 points with s2 = 0.09. The researcher would like to use the sample to estimate how much effect the workshop would have for the entire college population. Which of the following is the 80% confidence interval for these data?
A) μD = 0.60 ± 0.09( 1.860)
B) μD = 0.60 ± 0.10(1.397)
C) μD = 0.60 ± 0.01(1.397)
D) μD = 0.60 ± 0.10( 1.860)
Answer:
B) μD = 0.60 ± 0.10(1.397)
Step-by-step explanation:
The confidence interval is given by:
[tex]MD±t_{\alpha/2, n-1} \frac{s}{\sqrt{n} }[/tex]
Where
MD=60
n=9
df=n-1=8
[tex]t_{\alpha/2, n-1}=1.397[/tex]
[tex]s=\sqrt{0.09} =0.3[/tex]
Then the confidence interval is
μD=0.60±1.397*(0.3/√9)
μD=0.60±0.10*(1.397)
You estimate that you have completed 1/4 of the work your boss expects this week. What precent if your work is complete?
Answer:
You have completed 25% of your work.
Step-by-step explanation:
Consider the provided information.
You estimate that you have completed 1/4 of the work.
To find the percentage of work complete simplify the fraction and multiply it with 100.
[tex]\frac{1}{4}=0.25[/tex]
Now multiply it by 100.
[tex]0.25\times 100=25\%[/tex]
Hence, you have completed 25% of your work.
A bag contains 99 red marbles and 99 blue marbles. Taking two marbles out of the bag, you:
• put a red marble in the bag if the two marbles you drew are the same color (both red or both
blue), and
• put a blue marble in the bag if the two marbles you drew are different colors.
Repeat this step (reducing the number of marbles in the bag by one each time) until only one
marble is left in the bag. What is the color of that marble?
The final marble left in the bag will be red.
Let, analyze the process step by step:
Initially, the bag contains 99 red marbles and 99 blue marbles.
When you take two marbles out of the bag, there are two possibilities: either you get two red marbles or two blue marbles, or you get one red and one blue marble.
a. If you get two marbles of the same color (both red or both blue), you put a red marble in the bag.
b. If you get one red and one blue marble, you put a blue marble in the bag.
After putting a marble back in the bag, you have one less marble in the bag.
You repeat this process, reducing the number of marbles in the bag by one each time, until only one marble is left in the bag.
Now, let's think about the outcomes at each step:
If the bag contains an odd number of marbles (99 red + 99 blue = 198), the final marble will be red because at each step, you are adding a red marble back to the bag.
If the bag contains an even number of marbles (e.g., 100 red + 100 blue = 200), the final marble will be blue because at each step, you are adding a blue marble back to the bag.
In this case, the bag contains 99 red marbles and 99 blue marbles, which is an odd number (198 marbles).
Therefore, the final marble left in the bag will be red.
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Please Help! I don't know where to start with this, please show all work!
What is the vertex form of the equation?
y = -x^2 + 12x - 4
Hey!
-------------------------------------
Formula's:
x_v = -b/2a
y_v = ax² + bx + c
-------------------------------------
Parabola Params:
a = -1
b = 12
c = 4
-------------------------------------
Solve for [tex]x_{v}[/tex]
[tex]x_{v} = \frac{-b}{2a}[/tex]
[tex]x_{v} = \frac{-12}{2(-1)}[/tex]
[tex]x_{v} = -6[/tex]
-------------------------------------
Solve for [tex]y_{v}[/tex]
Use -6 for [tex]x_{v}[/tex]
[tex]y_{v} = -6^2 + 12(6) - 4\\[/tex]
[tex]y_{v} = -36 + 72 - 4[/tex]
[tex]y_{v} = 32[/tex]
-------------------------------------
Answer:
(6, 32)
-------------------------------------
Hope This Helped! Good Luck!
Mike recently increased the size of his Jeep tires from the original 29 inch diameter to the larger 33.73 inch diameter. If Mike didn't recalibrate his speedometer, how fast is he really going on the new tires when his speedometer shows he is traveling 60 mph?
a. 54.5 mph
b. 62.1 mph
c. 66.1 mph
d. 69.8 mph
Answer:
d. 69.8 mph
Step-by-step explanation:
Since, the ratio of the diameter of the tyre of a vehicle and its speed must be constant,
Given,
The original diameter of the tyre = 29 inch,
Original speed = 60 mph,
Thus, the ratio of diameter and the speed of the vehicle = [tex]\frac{29}{60}[/tex]
New diameter of the tyre = 33.73 inch,
Let x be the new speed of the vehicle = [tex]\frac{33.73}{x}[/tex]
[tex]\implies \frac{29}{60}=\frac{33.73}{x}[/tex]
[tex]\implies x=\frac{33.73\times 60}{29}=69.79\approx 69.8\text{ mph}[/tex]
Hence, the actual speed of the vehicle would be 69.8 mph.
OPTION D is correct.
4. Corrupt professor Z has a class of 50 students. He needs to give exactly 10 A's. However five students already have a special deal (they are professor Z's nephews and nieces) and will get A's for sure. How many ways can the 10 A's be distributed?
Answer:
Step-by-step explanation:
Given that the professor Z has a class of 50 students is corrupt. However five students already have a special deal (they are professor Z's nephews and nieces) and will get A's for sure.
Thus out of 10 students 5A's are reserved
Remaining 5 can be distributed in
I 5 to any one of the 45, II to any one of the 44....
i.e. 45P5 ways
no of ways = 45P5 == 146611080
An irrational number is a real number and an integer.
True
False
Answer:
A real number is a number that is somewhere on a number line, so any number on a number line that isn't a rational number is irrational. The square root of 2 is an irrational number because it can't be written as a ratio of two integers
hope it helps!!
Step-by-step explanation:
PLEASE HELP What is the equation in standard form of a parabola with a focus of (-3,2) and a directrix of y=4.
Graphing y = 4 and the focus, we clearly see that the equation we need has the form (x - h)^2 = 4a(y - k).
We need to find a, h and k.
The focus is half way between the vertex and directrix.
You know that y = 4 is 2 units away from the focus and the focus is 2 units down from the focus. So, our vertex is (-3, 0).
From the vertex to the directrix, there are 4 units. Half that distance is the value of a. So, a = 2.
We have all that is needed to form our equation.
(x - (-3))^2 = 4(2)(y - 0)
(x + 3)^2 = 8y
Done.
Answer:
i think this will help (x - (-3))^2 = 4(2)(y - 0)
(x + 3)^2 = 8y
Step-by-step explanation:
Use the discriminant to describe the roots of each equation. Then select the best description.
x^2 - 4x + 4 = 0
double root
real and rational root
real and irrational root
imaginary root
Answer:
Hello My Friend! The correct answer its double root.
Step-by-step explanation:
In this equation, if we applie the a, b and c coefficients (a=1, b=4, c=4) ind the Bhaskara, the final result will be 4 for both cases. x'=4 and x''=4. It happens because the number of theta is equal to 0. So, both roots will be the same number.
Given the coordinates of the vertices of a quadrilateral, determine whether it is a square, a rectangle, or a parallelogram. Then find the perimeter of the quadrilateral. A(6, –4), B(11, –4), C(11, 6), D(6, 6)
Answer:
The answer to your question is: it's a rectangle
perimeter = 30 u
Step-by-step explanation:
d = √((x2.x1)² + (y2-y1)²)
Now, calculate the distances AB, BC, CD, AD
dAB = √((11-6)² + (-4+4)² = √5² = 5
dBC = √((11-11)² + (-4-6)² =√10 = 10
dCD = √((6-11)² + (6-6)² = √5² = 5
dAD = √((6-6)² + (6+4)² = √10² = 10
From the results we conclude that is a rectangle because two sides have the same length and the other two also measure the same. We can draw it to confirm this.
Perimeter = dAB + dBC + dCD + dAD
= 5 + 10+ 5 + 10 = 30 units
To determine the shape of the quadrilateral, calculate the distances between the vertices and check for equal side lengths and 90-degree angles. The given quadrilateral is a parallelogram since the opposite sides are parallel and equal. The perimeter of the quadrilateral is 30 units.
Explanation:To determine whether the given quadrilateral is a square, a rectangle, or a parallelogram, we can use the properties of each shape. A square is a quadrilateral with all sides equal in length and all angles equal to 90 degrees. A rectangle is a quadrilateral with opposite sides equal in length and all angles equal to 90 degrees. A parallelogram is a quadrilateral with opposite sides parallel and equal in length. To find the perimeter of the quadrilateral, we can calculate the sum of the lengths of all four sides.
Calculating the distances between each pair of given points:
Distance between A and B: √[(11-6)² + (-4-(-4))²] = √(5² + 0) = √25 = 5Distance between B and C: √[(11-11)² + (6-(-4))²] = √(0 + 100) = 10Distance between C and D: √[(6-11)² + (6-6)²] = √((-5)² + 0) = √25 = 5Distance between D and A: √[(6-6)² + (6-(-4))²] = √(0 + 100) = 10The distances between the vertices are: AB = 5, BC = 10, CD = 5, and DA = 10. Therefore, the perimeter of the quadrilateral is 5 + 10 + 5 + 10 = 30 units.
At the end of year X, automobile installment credit accounted for 36 percent of all outstanding consumer installment credit. At that time automobile finance companies extended $57 billion of credit, or \small \frac{1}{3} of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that time?A. 62B. 171C. 475D. 513E. 684
Answer:
option (c) 475
Step-by-step explanation:
let the automobile installment credit be 'C'
Given:.
Automobile installment credit accounted for 36 percent of all outstanding consumer installment credit
Now,
57 billion is [tex]\frac{1}{3}[/tex] of automobile installment credit
or
57 billion = [tex]\frac{1}{3}[/tex] × C
or
C = 57 × 3
or
C = 171 billion
now,
installment credit accounted = 36% of all outstanding consumer installment credit
or
171 billion = 0.36 × all outstanding consumer installment credit
or
All outstanding consumer installment credit = $475 billion
Hence, the correct answer is option (c) 475
What is the degree of the polynomial 5a6bc2+8d5+7e6f2−10g4h7 ? Enter your answer in the box.+
Answer:
11
Step-by-step explanation:
The degree of a polynomial is he highest of the degrees of its monomials (individual terms) with non-zero coefficients.
You are given the polynomial
[tex]5a^6bc^2+8d^5+7e^6f^2-10g^4h^7[/tex]
It consists of 4 terms:
[tex]5a^6bc^2[/tex][tex]8d^5[/tex][tex]7e^6f^2[/tex][tex]-10g^4h^7[/tex]The degrees are:
of the first term is [tex]6+1+2=9[/tex]of the second term is [tex]5[/tex]of the third term is [tex]6+2=8[/tex]of the fourth term is [tex]4+7=11[/tex]The greatest degree is 11.
Answer:
11
Step-by-step explanation:
I did the quiz
What value of x makes the equation true?
1/2 (4x−5)+5/2=10 (Btw, the numbers 1/2 and 5/2 are fractions)
A. 5
B. 8
C. 12
D. 20
Answer:
x= 5 fam trust
Step-by-step explanation:
plug it in brainliest plzzzzzzzzzzzzzzzzz
What is the least angle measure by which this figure can be rotated so that it maps onto itself?
45°
90°
180°
360°
Answer:
The correct answer is 90
Step-by-step explanation:
A blueprint shows a house with two fences. Fence A is 1 4/5 inches long on the blueprint and is to be 1 1/2 feet long. How long is Fence B on the blueprint?
The problem is about finding a length on a blueprint using scale factor. A ratio is established between blueprint measurements and real-life measurements. However, information about Fence B's actual size is needed to calculate its blueprint length.
Explanation:The subject of this question is mathematics, more specifically proportionality and scale factor. To solve this problem, you need to establish the ratio or scale represented by the blueprint to the actual size. In the given problem, 1 4/5 inches on the blueprint represents 1 1/2 feet in real life. First, convert the measures to improper fractions to easily manage the computations. Hence, 1 4/5 becomes 9/5 inches and 1 1/2 feet becomes 3/2 feet. The scale becomes 9/5 inches:3/2 feet on blueprint:real life. Now, we need additional information about the actual size of Fence B to calculate its length on the blueprint.
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PLEASE HELP!!!!
WILL GIVE BRAINLY
Which statements are true?
Select each correct answer.
9g3+12=3(3g3+4)
35g5−25g2=5g2(7g3−5)
24g4+18g2=6g2(4g2+3g)
4g2−g=g2(4−g)
Billy estimates that they will sell approximately 250 burgers thisweekend how much burger meat and fries (in pounds) should he order to be prepared for this weekend
Answer:
300 Burgers
Step-by-step explanation:
Since the question gives us an approximation of 250 burgers, we can round the number to 300. This is only because they had a estimation of 250 and would like to be prepared for the weekend. Being prepared would consist of ordering more than expected to make sure the burgers do not run out.
Three parking attendants are required to park cars for each blue lot , while two can handle each red lot. Of the 15 lots that will be used for tonight, 60% are blue and 40% are red. How many parking attendants are required for tonight's event
Answer:
[tex]39\ parking\ attendants[/tex]
Step-by-step explanation:
Let
x -----> the number of blue lots
y-----> the number of red lots
we know that
[tex]x+y=15[/tex] ------> equation A
we have that
[tex]x=0.60(15)=9\ blue\ lots[/tex]
[tex]y=0.40(15)=6\ red\ lots[/tex]
The total parking attendants required for tonight's event is equal to the product of the number of blue lots by three plus the product of the number of red lots by two
so
[tex]9(3)+6(2)=39\ parking\ attendants[/tex]
Answer:
39
Step-by-step explanation:
Marc is decorating 60 cupcakes for a school fund-raiser. He starts working at 1:00 P.M. In the afternoon, first setting up his supplies and then starting to decorate. At 1:05 P.M. He has 5 cupcakes decorated. At 1:08 P.M. He has 10 cupcakes decorated. If he decorates cupcakes at a constant rate, at what time that afternoon will he finish decorating the 60 cupcakes?
Answer:
1.38 pm.
Step-by-step explanation:
After 1.05 PM the rate at which he decorates the cakes is 10 - 5 = 5 cakes per 3 minutes = 5/3 cakes per minute. At 1.08 pm he has made 10 cupcakes.
At 1.08 he has to decorate another 50 cakes so the time he will take to do these is 50 / 5/3 = 50 * 3/5 = 30 minutes.
So the time when he finishes 60 cupcakes is 1.08 + 30
= 1.38 pm.
The 60 cupcakes will be decorated at 1.38 pm.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
After 1.05 PM the rate at which he decorates the cakes is 10 - 5 = 5 cakes per 3 minutes = 5/3 cakes per minute. At 1.08 pm he made 10 cupcakes.
At 1.08 he has to decorate another 50 cakes so the time he will take to do these is 50 / 5/3 = 50 * 3/5 = 30 minutes.
The time when he finishes 60 cupcakes is:-
1.08 + 30 = 1.38 pm.
Therefore, 60 cupcakes will be decorated at 1.38 pm.
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What are the coordinates of the hole in the graph of the function?
Answer:
The answer to your question is: (5/2, -6)
Step-by-step explanation:
Given f(x) = (6x - 36) / (2x² - 17x + 30)
Factorize both, numerator and denominator
Numerator = 6(x - 6)
Denominator = 2x² - 12x - 5x + 30
= 2x(x - 6) - 5(x - 6)
= (x - 6) (2x - 5)
Now f(x) = 6(x - 6) / (x - 6) (2x - 5) Cancel (x - 6)
f(x) = 6 / 2x - 5
Find the hole 2x - 5 = 0
2x = 5
x = 5/2
In 5/2 there is a hole, in y is approximately -6
-7y-4x=1
7y-2x=53
solve for system of equations
Answer:
x = -9
y = 35/7
Step-by-step explanation:
Given equations :-
-7y - 4x = 1 ....... ( i )
7y - 2x = 53 ........ ( ii )
From ( i )
-7y = 1 + 4x
[tex]y = \frac{ - (1 + 4x)}{7} [/tex]
..........( iii )
From ( ii )
7y - 2x = 53
7y = 53 + 2x
[tex]y = \frac{53 + 2x}{7} [/tex]
.......( iv )
Equating both ( iii ) & ( iv )
y = y
[tex] \frac{ - (1 + 4x)}{7} = \frac{53 + 2x}{7} [/tex]
-(1 + 4x ) = 53 + 2x
-1 -4x = 53 + 2x
-1 - 53 = 2x + 4x
-54 = 6x
-54/6 = x
-9 = x
Also,
[tex]y = \frac{ - (1 + 4x)}{7 } \\ \\ y = - \frac{(1 + 4( - 9))}{7} [/tex]
[tex]y = - \frac{ (1 - 36)}{7} \\ \\ y = - \frac{( - 35)}{7} \\ \\ y = \frac{35}{7} [/tex]
| A retiree invests $8,000 in a savings plan that pays
4% per year. What will the account balance be at
the end of the first year?
Answer:
8320
Step-by-step explanation:
(100%+4%)8000=8320
The balance at the end of the first year of the investment will be $8320, which includes the initial investment of $8000 and the interest earned, calculated as 4% of the initial investment.
Explanation:This is a basic interest problem in mathematics. To calculate the balance at the end of the first year, we need to add the initial investment to the amount earned through interest. The interest earned is the product of the initial investment and the interest rate.
In this case, the initial investment is $8000 and the interest rate is 4% per year or 0.04 in decimal form. So, the interest earned would be the product of $8000 and 0.04, which equals $320.
Therefore, the balance at the end of the first year would be the initial investment plus the interest earned, which is $8000 + $320 = $8320.
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What is the geometric relationship between u, minusv, and uminusv?
A. The vectors u, minusv, and uminusv form a right triangle.
B. The vectors u, minusv, and uminusv form a parallelogram whose other vertex is at 0.
C. The vectors u, minusv, and uminusv form an equilateral triangle.
D. The vectors u, minusv, and uminusv form a parallelogram whose other vertex is at uplusv.
Answer:
C. The vectors u, minusv, and uminusv form a parallelogram whose other vertex is at 0.
Step-by-step explanation:
We draw the vector u=A at the origin of a Cartesian plane. then at the same point, we draw -v = -B. To find the vector that represents u-v = A-B, straight lines are drawn parallel to each vector, forming a parallelogram. The resulting vector will be the diagonal of the parallelogram that begins at the origin of the plane.
Choose all of the angles that are coterminal with -150°.
-510°
-210°
150°
210°
570°
Answer:
210, 150
Step-by-step explanation:
Answer:
-510, 210 and 570.
Step-by-step explanation:
I'm on the same assignment right now! If you draw them you will see that those are the answers.
During the year, FastDry Corporation has $ 340,000 in revenues, $ 155,000 in expenses, and $ 12,000 in dividend declarations and payments. Net income for the year was:
Answer:
$185,000
Step-by-step explanation:
We have been been given that during the year, Fast Dry Corporation has $ 340,000 in revenues, $ 155,000 in expenses, and $ 12,000 in dividend declarations and payments.
We will use following formula to solve our given problem.
[tex]\text{Net income}=\text{Revenues}-\text{Expenses}[/tex]
[tex]\text{Net income}=\$340,000-\$155,000[/tex]
[tex]\text{Net income}=\$185,000[/tex]
Therefore, the net income for the year was $185,000.
Write the equation of the line perpindicular to the graph of 2x-5y=0 that passes through the point (-2,3)
Answer:
5x-2y=-4
Step-by-step explanation:
2x-5y=0
eq. of line perpendicular to ax+by=c is bx-ay=d,d is calculated by the given condition.
line perpendicular to 2x-5y=0 is 5x+2y=c
if it passes through (-2,3) ,then
5*-2+2*3=c
c=-10+6=-4
reqd. eq. is 5x+2y=-4
The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sample of 300 circuits is tested, revealing 14 defectives. Calculate a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool. Round the answers to 4 decimal places.
Answer: [tex](0.0228\ ,0.0706)[/tex]
Step-by-step explanation:
Given : Sample size : n= 300
The sample proportion of defectives : [tex]\hat{p}=\dfrac{14}{300}=0.0467[/tex]
Significance level for 95% confidence level =[tex]\alpha=1-0.95=0.05[/tex]
Critical z-value:[tex]z_{\alpha/2}=\pm1.96[/tex]
Confidence interval for population proportion :
[tex]\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]= 0.0467\pm (1.96)\sqrt{\dfrac{0.0467(1-0.0467)}{300}}[/tex]
[tex]\approx\ 0.0467\pm 0.0239\\\\=(0.0467-0.0239\ , \ 0.0467-0.0239)\\\\=(0.0228\ ,0.0706)[/tex]
Hence, a 95% two-sided confidence interval on the fraction of defective circuits produced by this particular tool= [tex](0.0228\ ,0.0706)[/tex]
Use differentiation rules to find the values of a and b that make the function f(x) = ( x 2 if x ≤ 2, ax3 + bx if x > 2 differentiable at x = 2.
To make the function differentiable at x = 2, we must ensure continuity by matching function values and differentiability by equating derivatives from both sides at x = 2. Solving the system of equations obtained from these conditions will give the values of a and b.
Explanation:To find the values of a and b that make the function f(x) = { x² if x ≤ 2, ax³ + bx if x > 2 } differentiable at x = 2, we need to ensure both continuity and differentiability of f(x) at this point. First, continuity at x = 2 requires that the limits from the left and the right are the same, meaning f(2) = 2² = 4 should equal a(2)³ + b(2). Second, for differentiability, the derivatives from the left and right at x = 2 must also be equal. The derivative of x² is 2x, so f'(2) = 4. Differentiating ax³ + bx gives 3ax² + b, so f'(2) = 12a + b must also equal 4. Solving these equations:
4 = 8a + 2b4 = 12a + bgives us a system of equations that when solved, will provide the exact values of a and b required.
Assume that a procedure yields a binomial distribution with a trial repeated n = 20 times. Use either the binomial probability formula (or technology) to find the probability of k = 14 successes given the probability p = 0.72 of success on a single trial.
Answer:
the probability is 0.1879
Step-by-step explanation:
If a procedure yields a binomial distribution, the probability of having k successes is given by:
[tex]P(k)=nCk*p^{k} *(1-p)^{n-k}[/tex]
Where nCk is calculated as:
[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]
Additionally, n is the number of trials and p is the probability of success in every trial.
Replacing, k by 14, n by 20 and p by 0.72 we get:
[tex]20C14=\frac{20!}{14!(20-14)!}=38,760[/tex]
[tex]P(k)=20C14*0.72^{14} *(1-0.72)^{20-14}[/tex]
[tex]P(k)=38,760*0.72^{14} *(1-0.72)^{20-14}\\P(k)=0.1879[/tex]
So, the probability is 0.1879
To find the probability of 14 successes given a binomial distribution with a trial repeated 20 times and a probability of success of 0.72 on a single trial, use the binomial probability formula.
Explanation:To find the probability of 14 successes given a binomial distribution with a trial repeated 20 times and a probability of success of 0.72 on a single trial, we can use the binomial probability formula. The formula is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Plugging in the values, we get:
P(X = 14) = C(20, 14) * 0.72^14 * (1 - 0.72)^(20 - 14)
Calculating this expression will give you the probability of 14 successes out of 20 trials.
Learn more about Binomial probability here:
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