The probability of A climbing the mountain is 1 / 3 and B climbing the mountain is 3 / 8. What is the probability that either one climbs the mountain?

The probability of A climbing the mountain is 1 / 3 and B climbing the mountain is 3 / 8. What is the probability that either one climbs the mountain? Correct Answer 11/24

Given:

P (A) = 1 / 3

P (B) = 3 / 8

Formula used:

P (U) = (P(A) × P’(B)) + (P’(A) × P(B))

P(A) = Probability of A event happening

P(B) = Probability of B event happening

Calculation:

P’ (A) = 2 / 3

P’ (B) = 5 / 8

⇒ P (U) = ((1 / 3) × (5 / 8)) + ((2 / 3) × (3 / 8))

⇒ P (U) = (5 / 24) + (6 / 24)

⇒ P (U) = 11 / 24

∴ Probability of either one climbing the mountain is 11/24

Key Points

P (U) = (P(A) × P’(B)) + (P’(A) × P(B))

P(A) = Probability of A event happening

P(B) = Probability of B event happening