One of the bartleby experts helped me with this Intro to Probability and Statistics homework problem. Below is the work that was provided by the expert. What I need to know is which distribution is being used?   Answer the following question about PMFs. Be sure to explicitly state which distribution you are using in each of the following cases. 1.  In a fair coin toss, what is the probability of getting exactly 3 heads in 5 tosses?     Work

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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One of the bartleby experts helped me with this Intro to Probability and Statistics homework problem. Below is the work that was provided by the expert. What I need to know is which distribution is being used?

 

Answer the following question about PMFs. Be sure to explicitly state which distribution you are using in each of the following cases.

1.  In a fair coin toss, what is the probability of getting exactly 3 heads in 5 tosses?

 

 

Work

 

Step 1: Write the given information
Let X be the number of heads and n be the number of tosses.
Given, the coin is fair. The probability of head is 2-0.5 and n=5.
Step 2: Find probability of getting exactly 3 heads in 5 tosses
The probability of head is constant for all tosses. The success is head and failure is tail. Each toss is
independent. Then, X follows binomial with n=5 and p=0.5
The PMF of X is
n
P(x)= (*) ² (1 p.) ',x=0,1.2...........n
Then, the probability of getting exactly 3 heads in 5 tosses is
(3)0.5³ (1-0.5)³-3
= 10×0.5³ x 0.5²
= 0.3125
P(X= 3) =
Solution
The probability of getting exactly 3 heads in 5 tosses is 0.3125
Transcribed Image Text:Step 1: Write the given information Let X be the number of heads and n be the number of tosses. Given, the coin is fair. The probability of head is 2-0.5 and n=5. Step 2: Find probability of getting exactly 3 heads in 5 tosses The probability of head is constant for all tosses. The success is head and failure is tail. Each toss is independent. Then, X follows binomial with n=5 and p=0.5 The PMF of X is n P(x)= (*) ² (1 p.) ',x=0,1.2...........n Then, the probability of getting exactly 3 heads in 5 tosses is (3)0.5³ (1-0.5)³-3 = 10×0.5³ x 0.5² = 0.3125 P(X= 3) = Solution The probability of getting exactly 3 heads in 5 tosses is 0.3125
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