Question

For three events, A, B and C, it is known that:

-A and C are independent

-B and C are independent

-A and B are mutually exclusive

-Pr(AUC) = 2/3, Pr(BUC) = 3/4, Pr(AUBUC) = 11/12

Find Pr(A), Pr(B) and Pr(C).

Answer 1

We first try to write mathematically what the three statements mean:
A and C are independent

B and C are independent

A and B are mutually exclusive

For simplicity let : P(A) = a, P(B) = b and P(C) = c.

Now, we are given that:

Similarly,

Also,

Substituting the value of c in equation (1), we get:

Substituting the value of c in equation (2), we get:

Thus,

P(A) = 1/3

P(B) = 1/2 ; and

P(C) = 1/2

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