Question

people with type o - negative blood are universal donors. any patient can receive a transfusion of o - negative blood. only 7.2% of the american population has o - negative blood.
if we choose 10 americans at random, what is the probability that at least 1 of them has o - negative blood?
(round to 3 decimal places. leave your answer in decimal form.)

Explanation:

Step1: Calculate the probability of none having O - negative blood

The probability that a single American does not have O - negative blood is \(1 - 0.072=0.928\).
For \(n = 10\) independent people, the probability that none of them has O - negative blood is \(P(X = 0)=(0.928)^{10}\).
Using a calculator, \((0.928)^{10}\approx0.479\).

Step2: Calculate the probability of at least 1 having O - negative blood

The probability of at least 1 having O - negative blood is \(P(X\geq1)=1 - P(X = 0)\).
Substitute \(P(X = 0)\approx0.479\) into the formula, we get \(P(X\geq1)=1 - 0.479 = 0.521\).

Answer:

\(0.521\)