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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?

Respuesta :

JeanaShupp

Answer: 0.516

Step-by-step explanation:

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

[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], 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 :-

[tex]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[/tex]

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

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