Question

Problem 4.28: People with type O-negative blood are

universaldonors. That is, any patient can receive a transfusion
ofO-negative blood. Only 7% of the American population
haveO-negative blood. If 10 people appear at random to give blood,
whatis the probability that at least 1 of them is a
universaldonor?

Answer 1

Answer: 0.516

Explanation:

Binomial probability distribution formula to find the probability of getting success in x trial:-

`P(x)=^nC_xp^x(1-p)^(n-x)`, where n is the number of trials , p is the probability of getting success in each trial.

Given : People with type O-negative blood are universal donors.

The proportion of the American population have O-negative blood =0.07

For n=10, the probability that at least 1 of them is a O-negative blood :-

`P(x\geq1)=1-P(x=0)\\\\=1-[^(10)C_0(0.07)^0(1-0.07)^(10)]\\\\=1-[(1)(1)(0.93)^(10)]\ \ \ [\text{ Since}^nC_0=1]\\\\=1-0.483982307179\approx1-0.4840=0.516`

Hence, the probability that at least 1 of them is a universal donor = 0.516