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 \(p = 1 - 0.072=0.928\).
For \(n = 10\) independent trials (choosing 10 Americans), the probability that none of them has O - negative blood is given by the binomial probability formula \(P(X = k)=C(n,k)\times p^{n - k}\times(1 - p)^{k}\). When \(k = 0\), \(C(n,k)=C(10,0)=\frac{10!}{0!(10 - 0)!}=1\). So \(P(X = 0)=(0.928)^{10}\).
Using a calculator, \((0.928)^{10}\approx0.479\).

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

The probability that at least 1 has O - negative blood is \(P(X\geq1)=1 - P(X = 0)\).
Since \(P(X = 0)\approx0.479\), then \(P(X\geq1)=1 - 0.479 = 0.521\).

Answer:

\(0.521\)