Gmat_mission wrote: ↑Sun Jun 14, 2020 1:59 pm
There is a 50% chance Walcir will visit Chile this year, while there is a 25% chance that he will visit Madagascar this year. What is the probability that Walcir will visit either Chile or Madagascar this year, but NOT both?
A. 25%
B. 50%
C. 62.5%
D. 63.5%
E. 75%
[spoiler]OA=B[/spoiler]
Solution:
Recall the formula for P(A or B) is:
P(A or B) = P(A) + P(B) - P(A and B)
The formula for P(A or B, but not both) is:
P(A or B, but not both) = P(A or B) - P(A and B)
P(A or B, but not both) = P(A) + P(B) - P(A and B) - P(A and B)
P(A or B, but not both) = P(A) + P(B) - 2 * P(A and B)
Using the above formula and assuming visiting one country is independent from visiting another, we have:
P(Chile (C) or Madagascar (M), but not both) = P(C) + P(M) - 2 * P(C and M)
P(C or M, but not both) = 0.5 + 0.25 - 2 * (0.5 * 0.25)
P(C or M, but not both) = 0.75 - 0.25
P(C or M, but not both) = 0.5
Answer: B
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