Question

According to a​ newspaper, 50% of bicycles stolen in a certain country are recovered. Find the probability​ that, in a sample of 9 randomly selected cases of bicycles stolen in the​ country, exactly 6 out of 9 bikes are recovered. The probability that exactly 6 out of 9 stolen bicycles are recovered is _____.

​(Type an integer or decimal rounded to three decimal places as​ needed.)

Answer 1

Solution:

Given:

p = probability of bicycles stolen in a certain country are recovered = 0.50

n = Number of bicycles stolen in the​ country randomly selected = 9

x = Number of bicycles stolen in a certain country are recovered follows a Binomial distribution with parameter n = 9 and p =0.5

We have to find:

P( exactly 6 out of 9 stolen bicycles are recovered ) =............?

P( X = 6) =............?

Binomial probability formula :

Where

q = 1- p = 1 - 0.5 = 0.5

Thus