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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鈭�B)=P(A鈭�B)脳P(B/A)

Complement rule: P(notA)=1鈭�P(A)

03

Step 3. Calculation

P(O)=7.2%=0.072

Complement rule:

P(notA)=1鈭�P(A)

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

P(notO)=1鈭�P(O)=1鈭�0.072=0928

Multiplication rule:

P(A鈭�B)=P(A)脳P(B)

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

P(10notO)=(P(notO))10=(0.928)10鈮�0.4737

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

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

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