25 the probability of a, b, c solving a problem are 1/3, 2/7, 3/8 respectively. if all the three try to solve the problem simultaneously, the probability that exactly one of them will solve it, is
Answers
The probability that exactly one of them will solve it, is 25/56.
Probability that A will solve the problem P(A) = 1/3
∴ Probability that A cannot solve the problem = P(A') = 1 - P(A) = 1 - 1/3 = 2/3
Probability that B will solve the problem P(B) = 2/7
∴ Probability that B cannot solve the problem = P(B') = 1 - P(B) = 1 - 2/7 = 5/7
Probability that C will solve the problem P(A) = 3/8
∴ Probability that C cannot solve the problem = P(C') = 1 - P(C) = 1 - 3/8 = 5/8
The problem needs to be solved exactly by one of them only. So it can be represented as:
(When A can solve it only AND others cant) OR (When B can solve it only AND others cant) OR (When C can solve it only AND others cant)
= [P(A) × P(B') × P(C')] + [P(A') × P(B) × P(C')] + [P(A') × P(B') × P(C)]
= [1/3 × 5/7 × 5/8] + [2/3 × 2/7 × 5/8] + [2/3 × 5/7 × 3/8]
= [25/168 + 20/168 + 30/168]
= 75/168
= 25/56
Required probability is 25/56.