Question

Based on data from the Greater New York Blood Program, when blood donors are randomly selected the probability of the having Group O blood is 0.45. Knowing that information, find the probability that AT LEAST ONE of the 5 donors has Group O blood type.

Answer 1

The probability that at least one of the 5 donors has Group O blood type is 0.9497.

Explanation:

We can model this as a binomial random variable, with n=5 (the sample size) and p=0.45.

The probability that exactly k donors have Group O blood type in the sample can be written as:

`P(x=k) = \dbinom{n}{k} p^(k)(1-p)^(n-k)\\\\\\P(x=k) = \dbinom{5}{k} 0.45^(k) 0.55^(5-k)\\\\\\`

We have to calculate the probability P(x≥1). In this case it easy to substract from 1 the probabitity that x is exactly 0:

`P(X\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{5}{0} p^(0)(1-p)^(5)=0.55^5=0.0503\\\\\\P(x\geq1)=1-0.0503=0.9497`