Question

In each of the following experiments, write the sample space S, number of sample points n(S), event A,B,C and n(A), n(B), n(C), also find complementary events, mutually exclusive events:

(ii) A die is thrown. A is the event that prime number comes up, B is the event that the number is divisible by three comes up, C is the event that the perfect square number comes up .

Answer 1

Given:
A die is thrown.
The sample space is {1, 2, 3, 4, 5, 6}.
∴ n(S) = 6
Now,
A is the event of getting a prime number.
∴ A = {2, 3, 5}
Or,
n(A) = 3
B is the event of getting a number that is divisible by 3.
∴ B = {3, 6}
Or,
n(B) = 2
C is the event of getting a number that is a perfect square.
∴ C = {1, 4}
Or,
n(C) = 2
Here,
A $\cap$ C = $\varnothing$
Thus, events A and C are mutually exclusive.