Question

According to a report from the Center for Studying Health System Change, 20% of Americans delay or go without medical care because of concerns about cost (The wall street journal, June 26, 2008). Suppose eight individuals are randomly selected.

The probability no one delays or goes without medical care is ____________ ;

The probability only one person delays or goes without medical care is ____________.
Please keep three decimals.

Answer 1

The probability no one delays or goes without medical care is 0.168;

The probability only one person delays or goes without medical care is 0.336.

Explanation:

This problem can be modeled with a binomial random variable, with sample size n=8 and probability of success p=0.2.

The probability that exactly k Americans delay or go without medical care because of concerns about cost within the sample of eight individuals can be calculated as:

`P(x=k) = \dbinom{n}{k} p^(k)(1-p)^(n-k)\\\\\\P(x=k) = \dbinom{8}{k} 0.2^(k) 0.8^(8-k)\\\\\\`

The probability no one delays or goes without medical care (x=0) is:

`P(x=0) = \dbinom{8}{0} p^(0)(1-p)^(8)=1*1*0.168=0.168\\\\\\`

The probability only one person delays or goes without medical care (x=1) is

`P(x=1) = \dbinom{8}{1} p^(1)(1-p)^(7)=8*0.2*0.21=0.336\\\\\\`