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.)
incorrect answer
0.522

Explanation:

Step1: Calculate the probability that none has 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, using the multiplication rule for independent events, the probability that all \(10\) do not have O - negative blood is \(P(\text{none})=(0.928)^{10}\).

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Step2: Calculate the probability that at least 1 has O - negative blood

Use the complement rule \(P(A)=1 - P(\text{not }A)\). Let \(A\) be the event that at least 1 has O - negative blood. Then \(P(A)=1 - P(\text{none})\).
Since \(P(\text{none})\approx0.474\), then \(P(A)=1 - 0.474 = 0.526\)

Answer:

\(0.526\)