1 of 36 tourists visiting namibia and S.A is chosen at random. The probability that he has been to S.A is 1/2,

Question

to namibia is 4/9, to neither is 1/3. Calculate the number of tourists to S.A, Namibia and to both.

Answer 1

The probability of tourists who never went to Namibia nor S.A would 1/3. That gives us a probability of 1 - 1/3 0r 2/3 for the tourists who went to either Namibia, S.A. or to both. Now, the probability of tourists who went to Namibia would be 4/9 and the probability of tourists who went to S.A. would be 1/2.

According to the definition of probability of union of 2 events,

P(Namibia or S.A.) = P(Namibia) + P(S.A) - P(Namibia and S.A.)
P(Namibia and S.A.) = P(Namibia) + P(S.A) - P(Namibia or S.A.)
P(Namibia and S.A.) = 4/9 + 1/2 - 2/3
P(Namibia and S.A.) = 5/18

Hope that helps.

Answer 2

12 have been to neither--1/3x36=12.
16 have been to Namibia--4/9x36=16
24 have been to SA or both, but at most 8 have not been to Namibia so, 8/16 =1/2 probability that you'll get someone who has been both places, if none was a woman.