Question

3. Joe is attempting basketball free throws. The probability of success on each attempt is 0.39 and his consecutive attempts are independent of each other. Answer the following questions. If Joe attempts three free throws, what is the probability he has at least one success? (a) Let X be the number of attempts required for Joe to observe his first successful free throw. What kind of discrete random distribution for X? (Binomial, Poisson, or none of them) (b) If Joe attempts 17 free throws, what is the probability he has exactly 7 successes?

4. Let Y be the number of times Paul gets the flu during one 12-month period. Y is Poisson with λ = 1.45. (a) List the possible values of Y. (b) What is the probability that Paul gets the flue at least once during the next 12-month period?

Answer 1

3)

Let X denote the number of success for Joe. Then X~Bin(n=3,p=0.39)

So, P(at least 1 success) =

a)

Let Y denote the number of attempts required to observe 1st success. Then Y would follow Geometric distribution.

Hence correct option would be none of them.

b)

Let L denote the number of success for Joe. Then X~Bin(n=17,p=0.39)

So,

4)

Let Y be the number of times Paul gets the flu during one 12-month period. Then

a)

So, the values that Y can take are 0,1,2,3,.....so on

b)