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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 at least 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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Verified Answer
A and B are required to solve a problem independently. If 1/2 and 1/3 ...
Probability that at least one of them solves the problem = P
P = 1 – 1/2 X 2/3 = 2/3
Most Upvoted Answer
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 A or B solves the problem, we can use the concept of complementary probability.
The probability that neither A nor B solves the problem is given by the product of their respective probabilities of not solving the problem:
P(not A) = 1 - P(A) = 1 - 1/2 = 1/2
P(not B) = 1 - P(B) = 1 - 1/3 = 2/3
Since A and B solve the problem independently, the probability that neither A nor B solves the problem is equal to the product of their individual probabilities:
P(neither A nor B) = P(not A) * P(not B) = (1/2) * (2/3) = 1/3
Therefore, the probability that at least one of A or B solves the problem is given by the complement of the probability that neither A nor B solves the problem:
P(at least one of A or B) = 1 - P(neither A nor B) = 1 - 1/3 = 2/3
Hence, the correct answer is option B) 2/3.
The probability that neither A nor B solves the problem is given by the product of their respective probabilities of not solving the problem:
P(not A) = 1 - P(A) = 1 - 1/2 = 1/2
P(not B) = 1 - P(B) = 1 - 1/3 = 2/3
Since A and B solve the problem independently, the probability that neither A nor B solves the problem is equal to the product of their individual probabilities:
P(neither A nor B) = P(not A) * P(not B) = (1/2) * (2/3) = 1/3
Therefore, the probability that at least one of A or B solves the problem is given by the complement of the probability that neither A nor B solves the problem:
P(at least one of A or B) = 1 - P(neither A nor B) = 1 - 1/3 = 2/3
Hence, the correct answer is option B) 2/3.
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