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 \(n = 10\) Americans, the probability that none of them has O - negative blood is \(P(X = 0)=0.928^{10}\).
Using the formula \(a^n\) (where \(a = 0.928\) and \(n = 10\)), we have \(0.928^{10}\approx0.479\).

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:

\(0.521\)