You are practicing your free throws for an upcoming basketball game. Every throw is successful with probability 2/3, independently of the others. Let X denote the number of successful throws out of 5. (a)  What kind of random variable is X? (Don’t forget the parameters.) (b)  What is the probability that you successfully make at least 3 out of the 5 free throws? (c)  Given that you successfully make at least 3 out of 5 free throws, what is the probability that you successfully make exactly 3 out of 5?

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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You are practicing your free throws for an upcoming basketball game. Every throw is successful with probability 2/3, independently of the others. Let X denote the number of successful throws out of 5.

  1. (a)  What kind of random variable is X? (Don’t forget the parameters.)

  2. (b)  What is the probability that you successfully make at least 3 out of the 5 free throws?

  3. (c)  Given that you successfully make at least 3 out of 5 free throws, what is the probability that you successfully make exactly 3 out of 5?

  4. (d)  What is the probability of scoring exactly 3 consecutive free throws within the set of 5?

  5. (e)  You keep practicing with sets of 5 free throws. What is the average number of sets until

    your first set where you miss every free throw?

Expert Solution
Step 1

Given that

n = 5 , p = 2/3

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Follow-up Question

You are practicing your free throws for an upcoming basketball game. Every throw is successful with probability 2/3, independently of the others. Let X denote the number of successful throws out of 5.

  1. (a)  What kind of random variable is X? (Don’t forget the parameters.)

  2. (b)  What is the probability that you successfully make at least 3 out of the 5 free throws?

  3. (c)  Given that you successfully make at least 3 out of 5 free throws, what is the probability that you successfully make exactly 3 out of 5?

  4. (d)  What is the probability of scoring exactly 3 consecutive free throws within the set of 5?

  5. (e)  You keep practicing with sets of 5 free throws. What is the average number of sets until

    your first set where you miss every free throw?

    could you finish d and e please
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