According to the Department of Health and Human Services, 30% of 18- to 25-year-olds have some form
of mental illness.
What is the probability AT LEAST one of six randomly
selected 18- to 25-year-olds have some form of mental
illness? Round to the nearest thousandth.

0.420

Explanation:

Given: The proportion of 18- to 25-year-olds have some form of mental illness: p= 0.30

Let x be the number of 18- to 25-year-olds that have mental illness.

A person can either have illness or not , so it follows Binomial distribution.

Probability distribution function:

, where n= samples oize , p probability of success in each trial , x= number of successes.

Here, n=6 ,

Required probability:

Hence, the probability at least one of six randomly  selected 18- to 25-year-olds have some form of mental  illness = 0.420