Question

Probability of solving specific problem independently by A and B are 1/2 and 1/3, respectively. If both try to solve the problem independently, find the probability that

(i) the problem is solved
(ii) exactly one of them solves the problem

Answer 1

i) Probability that the problem is solved is 0.67.

ii) Probability that exactly one of them solves the problem is 0.50.

The probability that the problem is solved is the probability that either A or B solves the problem, or both of them solve the problem. This can be calculated using the following formula:

P(A or B) = P(A) + P(B) - P(A and B)

where:

P(A) is the probability that A solves the problem

P(B) is the probability that B solves the problem

P(A and B) is the probability that both A and B solve the problem

In this case, P(A) = 1/2, P(B) = 1/3, and P(A and B) = (1/2)(1/3) = 1/6. Plugging these values into the formula, we get:

P(A or B) = (1/2) + (1/3) - (1/6) = 5/6

Therefore, the probability that the problem is solved is 5/6.

The probability that exactly one of them solves the problem can be calculated using the following formula:

P(exactly one of A and B) = P(A) + P(B) - 2P(A and B)

In this case, P(exactly one of A and B) = (1/2) + (1/3) - 2(1/6) = 1/2.

Therefore, the probability that exactly one of them solves the problem is 1/2.