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Answer:
Step-by-step explanation:
a) The probability that all three applicants will be admitted is 0.5 * 0.5 * 0.5 = 0.125, or 12.5%. (b) The probability that none of the three applicants will be admitted is the complement of all three being admitted. So, it's 1 - 0.125 = 0.875, or 87.5%.(c) To find the probability that only one applicant will be admitted, we need to consider three cases: the first applicant is admitted while the other two are not (0.5 * 0.5 * 0.5 = 0.125), the second applicant is admitted while the other two are not (0.5 * 0.5 * 0.5 = 0.125), and the third applicant is admitted while the other two are not (0.5 * 0.5 * 0.5 = 0.125). Adding these probabilities together gives a total probability of 0.375, or 37.5%.When dealing with independent events like these, the probabilities of different outcomes are multiplied when finding the probability of multiple events happening together. Complementary probabilities are used to find the probability of events not happening. In the case of "only one admitted," we account for each of the three applicants separately. This approach ensures a comprehensive analysis of the possible outcomes and their associated probabilities.