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Chapter 5: Q 91. (page 331)

Universal blood donors People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7.2%, of the American population have O-negative blood. If 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor? Follow the four-step process.

Short Answer

Expert verified

P (at least one O) = 52.63%

Step by step solution

01

Step 1. Given Information

Because O-negative blood donors are universal, 7.2 percent of the American population has O-negative blood.

02

Step 2. Concept used

Multiplication rule:P(A∩B)=P(A∩B)×P(B/A)

Complement rule: P(notA)=1−P(A)

03

Step 3. Calculation

P(O)=7.2%=0.072

Complement rule:

P(notA)=1−P(A)

To determine the likelihood of not having type O, use the complement rule:

P(notO)=1−P(O)=1−0.072=0928

Multiplication rule:

P(A∩B)=P(A)×P(B)

To find the likelihood of 10people not possessing type O, use the multiplication rule:

P(10notO)=(P(notO))10=(0.928)10≈0.4737

To calculate the likelihood of finding at least one individual with type O, use the complement rule:

P(atleastoneO)=1−P(10notO)P(atleastoneO)=1−0.4737P(atleastoneO)=0.5263=52.63%

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Most popular questions from this chapter

Teachers and college degrees Select an adult at random. Define events A: a person has earned a college degree, and T: person’s career is teaching. Rank the following probabilities from smallest to largest. Justify your answer.

P(A)P(T)P(A|T)P(T|A)

You want to estimate the probability that the player makes 5or more of 10shots. You simulate 10 shots 25 times and get the following numbers of hits:

5754153434534463417455657 What is your estimate of the probability?

(a) 5/25, or 0.20 (d) 16/25, or 0.64

(b) 11/25, or 0.44 (e) 19/25, or 0.76

(c) 12/25, or 0.48

Box of chocolates According to Forrest Gump, “Life is like a box of chocolates. You never know what you’re gonna get.” Suppose a candy maker offers a

special “Gump box” with 20 chocolate candies that look the same. In fact, 14 of the candies have soft centers and 6 have hard centers. Choose 2 of the

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To simulate whether a shot hits or misses, you would assign random digits as follows:

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