Concept explainers
Of the volunteers donating blood in a clinic, 80% have the Rhesus (Rh) factor present in their blood.
- a If five volunteers are randomly selected, what is the
probability that at least one does not have the Rh factor? - b If five volunteers are randomly selected, what is the probability that at most four have the Rh factor?
- c What is the smallest number of volunteers who must be selected if we want to be at least 90% certain that we obtain at least five donors with the Rh factor?
a
Find the probability that at least one does not have the Rh factor, if five volunteers are randomly selected.
Answer to Problem 61E
The probability that at least one does not have the Rh factor, if five volunteers are randomly selected is 0.6723.
Explanation of Solution
Calculation:
A random variable Y is a binomial distribution based on n trails with success probability p if and only if,
The random variable Y is defined as the number of volunteers with Rh factor. The number of volunteers selected is
The probability is,
Hence, the probability that at least one does not have the Rh factor, if five volunteers are randomly selected is 0.6723.
b
Find the probability that at most four have the Rh factor, if five volunteers are randomly selected.
Answer to Problem 61E
The probability that at most four have the Rh factor, if five volunteers are randomly selected is 0.6723.
Explanation of Solution
Calculation:
The probability is,
Hence, the probability that at most four have the Rh factor, if five volunteers are randomly selected is 0.6723.
c
Find the smallest number of volunteers who must be selected if there is at least 90% certain that we obtain at least five donors with the Rh factor.
Answer to Problem 61E
The smallest number of volunteers who must be selected if there is at least 90% certain that we obtain at least five donors with the Rh factor is 8.
Explanation of Solution
Calculation:
The probability for at least five donors with the Rh factor is,
The probability for
The probability for
The probability for
The probability for
The probability value when
Hence, the smallest number of volunteers who must be selected if there is at least 90% certain that we obtain at least five donors with the Rh factor is 8.
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Chapter 3 Solutions
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