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A problem in calculus is given to two students A and B whose chances of solving it are 1/3 and1/4 respectively. Find the probability of the problem being solved if both of them try independently.

A problem in calculus is given to two students A and B whose chances of solving it are
1/3
and1/4
respectively. Find the probability of the problem being solved if both of them try
independently.

Grade:upto college level

1 Answers

Latika Leekha
askIITians Faculty 165 Points
6 years ago
The probability that the problem is solved by A = P(A) = 1/3
Hence, the probability that it is not solved by A = P(AC) = 1-1/3 = 2/3
The probability that the problem is solved by B = P(B) = 1/4
Hence, the probability that it is not solved by B = P(BC) = 1-1/4= 3/4
P (that the problem is solved) = P(A) P(BC) + P(B) P(AC) + P(A) P(B)
= 1/3 . 3/4 + 1/4. 2/3 + 1/3 .¼
= 1/4 + 1/4 + 1/3 .1/4
= 6/12
= 1/2
Hence, the probability that the problem is solved is 1/2.
Thanks & Regards
Latika Leekha
askIITians Faculty

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