Can someone help me figure this math question out?

Question

One of 36 tourists on holiday in Namibia and South Africa is chosen at random.

The probability that he has been to South Africa before is 1/2

.

The probability that he has been to Namibia before is 4/9

.

The probability that he has been to neither country before is 1/3

what is the probability that he has been to both countries before?

how do i solve this?

.

Answer 1

the probability of him to visit in both countries is 2/3 because it's the opposite of 1/3 of him that he has been to neither countries.

Answer 2

The probability that he has been to neither country is 1/3

So, The probability that he has been to at least one country is 2/3

You can solve this using sets.

Let A = set of all people been to SA

B = set of all people been to Namibia

AUB = set of all people been to at least one of the countries

AnB = set of all people been to both coutnries.

n(A) = (1/2)*36 = 18

n(B) = (4/9)*36 = 16

n(AUB) = (2/3)*36 = 24

n(AnB) = n(A) + n(B) - n(AUB)

           = 18 + 16 - 24

           = 10

P(both countries) = 10/36 = 5/18

Answer 3

Draw a Venn Diagram. It may help.

P(neither)=1/3=12

We now have 24 remaining who have been to South Africa and/or Namibia.

P(SA)=1/2=18

P(N)=4/9=16

24 is made up of 18 and 16, so the intersection of those must be 10.

10/36 or 5/18 is the probability that he has been to both countries before.

Answer 4

Since the probability that he has been to South Africa before is (1/2) and the probability that he has been to Namibia before is (4/9), the probability that he has been to both is:

(1/2) x (4/9) = 4/18 = 2/9 = .222222222222222   <<<<<

BTW, the 36 tourists is irrelevant and the fourth statement is not only irrelevant but it also contradicts the two statements before it.

According to the 1/2 and 4/9, the probability that he has been to neither country before is [1 - (1/2)] x [1 - (4/9)] = (1/2) x (5/9) = (5/18)

Answer 5

10/36 = 5/18

how, you may ask.. (actually, you did ask!)

P(South Africa) = 1/2 ==> 18 have been to SA

P(Nambia) = 4/9 ==> 16 have been to Nambia

P(neither) = 1/3 ==> 12 have been to neither

this gives 18 + 16 + 12 = 46 people

but there are only 36, which means that the difference of 10 have been to both

10/36 is the probability that the person has been to both, which reduces to 5/18

You can verify this with a Venn diagram:

10 have been to both

8 have been to SA only (==> 18 to SA ==> P(SA)= 1/2)

6 have been to Nambia only(==> 16 to Nam ==> P(N) = 4/9)

this is 24 people, which means that 12 have been to neither (so P(Neither)= 12/36 = 1/3)