Question

A basketball player has a 50% success rate in free throw shots. Assuming that the outcomes of all free throws are independent from one another, what is the probability that, within a sequence of 20 shots, the player can score five baskets in a row?

Answer 1

Answer:0.0869 %

Explanation:

Given

probability of getting success is 50 % i.e. 0.5

So probability of missing the throw is 0.5

For 20 shots probability that he can score five baskets

Using Binomial distribution

$^nC_r=\frac{n!}{\left ( n-r\right )!\left ( r\right )!}$

here n=20

p=0.5 (Probability of winning)

q=0.5 (Probability of loosing)

for r=5

$^20C_5\left ( 0.5\right )^5\left ( 0.5\right )^{15}=\frac{20!}{\left ( 20-5\right )!\left ( 5\right )!}\times \left ( 0.5\right )^5\left ( 0.5\right )^{15}$

$=19\times 6\times 4\times 2\times 0.5^20=0.0008697$

i.e. 0.0869 %