A and B are required to solve a problem independently. If 1/2 and 1/3 are their respectively probabilities of solving the problem, then the probability that atleast one of them solves the problem.
a)
1/3
b)
2/3
c)
1/2
d)
1/4
Correct answer is option 'B'. Can you explain this answer?

Question

A and B are required to solve a problem independently. If 1/2 and 1/3 are their respectively probabilities of solving the problem, then the probability that atleast one of them solves the problem.

a)
1/3
b)
2/3
c)
1/2
d)
1/4

Correct answer is option 'B'. Can you explain this answer?

Answer

To find the probability that at least one of them solves the problem, we can use the concept of complementary probability. The complementary probability of an event A is equal to 1 minus the probability of the event not happening (A'). In this case, let's find the probability that neither A nor B solves the problem.

Probability that A does not solve the problem (A'):
A' = 1 - 1/2 = 1/2

Probability that B does not solve the problem (B'):
B' = 1 - 1/3 = 2/3

Since A and B are solving the problem independently, the probability that neither A nor B solves the problem is given by the product of their respective complementary probabilities.

Probability that neither A nor B solves the problem (A' and B'):
(A' and B') = A' * B' = (1/2) * (2/3) = 1/3

Now, we can find the probability that at least one of them solves the problem by subtracting the probability that neither A nor B solves the problem from 1.

Probability that at least one of them solves the problem:
= 1 - (A' and B')
= 1 - 1/3
= 2/3

Therefore, the correct answer is option B) 2/3.

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