Question

basketball player who ordinarily makes about 55% of his free throw shots has made 4 in a row. Is this evidence that he has a "hot hand" tonight? That is, is this streak so unusual that it means the probability he makes a shot must have changed? Expla

Answer 1

Answer:

Step-by-step explanation:

Given that a basketball player who ordinarily makes about 55% of his free throw shots has made 4 in a row.

Probability for a success in any random throw = $55%=0.55$

Since each throw is independent no of successive throws is binomial with

p = 0.55 and q = 0.45

Probability his free throw shots has made 4 in a row

= Prob that continuous succesees in 4 throws

=$(0.55)^4\\=0.09150125$

which shows that this is a very rare event with 0.55 for each success.

Hence this is unusual and there is a necessity to increase 0.55 or 55%