Question

A and B are two independent events. The probability that A and B occur is 1/6 and the probability that neither of them occurs is 1/3. Find the probability of occurrence of two events.

Answer 1

P(A ∩ B) = \(\cfrac16\)

6P(A)² – 5P(A) + 1 = 0

6P(A)² – 3P(A) – 2P(A) + 1 = 

[2P(A) – 1][3P(A) – 1] = 0

2P(A) – 1 = 0

2P(A) = 1

P(A) = \(\cfrac12\)

3P(A) – 1 = 0

3P(A) = 1