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The probability a randomly selected person in the U.S. has blood type O- is 0.08. If 12 persons in the U.S. are randomly selected, what is the probability that exactly 3 have blood type O-?

a. 0.012
b. 0.002
c. 0.072
d. 0.192

User Hex C
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Final answer:

The probability that exactly 3 out of 12 randomly selected persons in the U.S. have blood type O- is found using the binomial probability formula and is 0.072.

Step-by-step explanation:

The student is asking about the probability of a specific event occurring among a certain number of trials, which is a common problem in probability theory. In this case, we are to determine the likelihood that exactly 3 out of 12 randomly selected individuals have blood type O-. This is a binomial probability problem because we have a fixed number of trials (12), two possible outcomes for each trial (having O- blood or not), and the probability of success (having O- blood) remains constant at 0.08 for each trial.

To solve this, we use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Where:

  • n = total number of trials (12)
  • k = number of successes we want (3)
  • p = probability of success on a single trial (0.08)
  • (n choose k) = binomial coefficient, which can be calculated as n! / (k!(n-k)!)

Substituting the values we get:

P(X = 3) = (12 choose 3) * 0.08^3 * (1-0.08)^(12-3) = 220 * 0.08^3 * 0.92^9

Calculating the above expression gives us the probability that exactly 3 out of 12 persons, randomly selected in the U.S., have blood type O-. The correct answer from the given options is (c) 0.072.

User Tsergium
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