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Math  /  Data & Statistics

Question10. 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 has O-negative blood. If 10 Americans are randomly selected, what is the probability that at least 1 of them is a universal donor? a) 0 b) 0.474 c) 0.526 d) 0.720 e) 1

Studdy Solution

STEP 1

1. The probability that a randomly selected American has O-negative blood is p=0.072 p = 0.072 .
2. The probability that a randomly selected American does not have O-negative blood is 1−p=0.928 1 - p = 0.928 .
3. We are selecting 10 Americans randomly.
4. We need to find the probability that at least one of them is a universal donor.

STEP 2

1. Calculate the probability that none of the 10 selected individuals has O-negative blood.
2. Use the complement rule to find the probability that at least one person has O-negative blood.

STEP 3

Calculate the probability that none of the 10 selected individuals has O-negative blood. This is given by:
(1−p)10=0.92810 (1 - p)^{10} = 0.928^{10}

STEP 4

Compute 0.92810 0.928^{10} :
0.92810≈0.476 0.928^{10} \approx 0.476

STEP 5

Use the complement rule to find the probability that at least one person has O-negative blood:
1−(0.92810)=1−0.476=0.524 1 - (0.928^{10}) = 1 - 0.476 = 0.524
The probability that at least one of the 10 randomly selected Americans is a universal donor is approximately:
0.524 \boxed{0.524}

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