Answer:
D. Neither group of colleges satisfies her criterion.
Step-by-step explanation:
The probability of admission to at least one of the colleges in the group is the complement of the probability of being admitted to none. That probability is the product of the probabilities of rejection from the colleges in the group.
<u>Group VW</u>
The probabilities of rejection from V and W are 0.6 and 0.75, so the probability of rejection by both is 0.6×0.75 = 0.45. The complement of that, the probability of admission to V or W (or both) is 1 - 0.45 = 0.55, which is less than 60%.
<u>Group XYZ</u>
The probabilities of rejection are 0.7, 0.8, and 0.8, so the probability of rejection by all of X, Y, and Z is 0.7×0.8×0.8 = 0.448. The complement of that, the probability of admission to X, Y, or Z is 1 -0.448 = 0.552, which is less than 60%.
Since neither group of colleges will have a probability of admission of 60% or more, neither group of colleges will satisfy her criterion.
