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.