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?

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A: We have given that  Probability mass function.  X 0 1 3 P(x) 0.4 0.2 0.4

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