Question

For an NBA player who makes 60% of all free throws, suppose that he shoots free throws independently.

1. Suppose that he shoots 6 free throws in a game. What is the probability that he scores more than 4 points?

2. If the player keeps shooting until he misses, what is the probability that he stops at the fourth trial?

3.If the player keeps shooting until he misses and let X denote the number of trials he shoots, what is E(X)? What is Var(X)?

Answer 1

1)

here this is binomial with parameter n=6 and p=0.6

probability that he scores more than 4 points =P(more than 4 shots)

probability =

P(X>=5)=

1-P(X<=4)=

1-∑x=04    (nCx)px(1−p)(n-x)    =

0.2333

2)this is geometric distribution with paramter p=1-0.6 =0.4

probability that he stops at the fourth trial =P(made first 3 and miss on 4th) =(0.6)³*0.4 =0.0864

3)E(X) =1/p=1/0.4 =2.5

varaince (X)=σ2=(1-p)/p2=

3.75