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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?
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A and B are required to solve a problem independently. If 1/2 and 1/3 ...
Probability that atleast one of them solves the problem = P
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A and B are required to solve a problem independently. If 1/2 and 1/3 ...
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.
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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