There is a 50% chance Walcir will visit Chile this year, while there is a 25% chance that he will visit Madagascar this

[Gmat_mission]

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]

Source: Veritas Prep

[Scott@TargetTestPrep]

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