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Molodets [167]
3 years ago
10

Based on data from the Greater New York Blood Program, when blood donors are randomly selected the probability of the having Gro

up O blood is 0.45. Knowing that information, find the probability that AT LEAST ONE of the 5 donors has Group O blood type.
Mathematics
1 answer:
Gnesinka [82]3 years ago
7 0

Answer:

The probability that at least one of the 5 donors has Group O blood type is 0.9497.

Step-by-step explanation:

We can model this as a binomial random variable, with n=5 (the sample size) and p=0.45.

The probability that exactly k donors have Group O blood type in the sample can be written as:

P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{5}{k} 0.45^{k} 0.55^{5-k}\\\\\\

We have to calculate the probability P(x≥1). In this case it easy to substract from 1 the probabitity that x is exactly 0:

P(X\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{5}{0} p^{0}(1-p)^{5}=0.55^5=0.0503\\\\\\P(x\geq1)=1-0.0503=0.9497

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This is the part missing:

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