Question

A problem in Mathematics is given to three students whose chances of solving it are 1/3, 1/4 and 1/5

(i) What is the probability that the problem is solved? 

(ii) What is the probability that exactly one of them will solve it?

Answer 1

Given P(A) = 1/3 

P(A') = 1 - 1/3 = 2/3

P(B) = 1/4 

P(B') = 1 - 1/4 = 3/4

and P(C) = 1/5 

P(C') = 1 - 1/5 = 4/5 

(i) P(A ∪ B ∪ C)

(ii) P(A ∩ B' ∩ C' or A' ∩ B ∩ C' or A' ∩ B' ∩ C')