Question

question 2 of 5
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 a person not having O - negative blood

The probability of a person having O - negative blood \(p = 0.072\). So the probability of a person not having O - negative blood \(q=1 - p=1 - 0.072 = 0.928\)

Step2: Calculate the probability that none of the 10 people have O - negative blood

Using the binomial probability formula \(P(X = k)=C(n,k)\times p^{k}\times q^{n - k}\), when \(k = 0\) and \(n = 10\), \(C(10,0)=\frac{10!}{0!(10 - 0)!}=1\), \(p = 0.072\), \(q = 0.928\), \(n = 10\). So \(P(X = 0)=1\times(0.072)^{0}\times(0.928)^{10}\)

$$P(X = 0)=(0.928)^{10}\approx0.478$$

Step3: Calculate the probability that at least 1 has O - negative blood

The probability that at least 1 has O - negative blood \(P(X\geq1)=1 - P(X = 0)\)

$$P(X\geq1)=1 - 0.478 = 0.522$$

Answer:

\(0.522\)