Is the statement correct? Show all work Joanne, a high school senior, has applie

Question

Is the statement correct? Show all work

Joanne, a high school senior, has applied for admission to four colleges, A, B, C, and D. She has estimated that the probability that she will be accepted for admission by college A, B, C, and D is 0.4, 0.3, 0.2, and 0.08, respectively. Thus, the probability that she will be accepted for admission by at least one college is

P(A) + P(B) + P(C) + P(D) = 0.4 + 0.3 + 0.2 + 0.08 = 0.98.

Correct, because

P(A) + P(B) + P(C) + P(D) = 0.98.

Incorrect, because

P(A) + P(B) + P(C) + P(D) 1.

    Incorrect, because the probabilities should be multiplied instead of added.Incorrect, because she forgot to divide by four to find the average.Incorrect, because these events are not mutually exclusive.

Explanation / Answer

Incorrect, because the probabilities should be multiplied instead of added.Incorrect, because she forgot to divide by four to find the average.Incorrect, because these events are not mutually exclusive.

Explanation:

because this assumes the events are mutually exclusive, and they are not.
To get the prob. of being accepted at least one college, you compute the prob. of being accepted at
NONE of the colleges, and then subtract from.
This is 1 -[(1-.4)(1-.3)(1-.2)(1-.08)] = 1 - .3091 = .6909.

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