According to a recent report, 0.20 is the probability that an American can identify nitrogen as the gas that makes up most of the earth's atmosphere.

Question

According to a recent report, 0.20 is the probability that an American can identify nitrogen as
the gas that makes up most of the earth's atmosphere. Six Americans are randomly selected. Find
the probability that exactly 2 of the 6 Americans can identify nitrogen as the gas that makes up
most of the earth's atmosphere.

Answer 1

The number of Americans (out of the 6) that can correctly identify nitrogen is a Binomial Distribution.

Let's denote this as X.

 

We want P[X = 2]:

 

P[X = 2] = (6 choose 2) (.2)² (1 - .2)⁴

 

6 choose 2 = 6! / [2!(6-2)!] ---> The number of ways of selecting 2 people out of 6 when order does not matter.

 

 

J.T.