41) A problem in mathematics is
given to three students A, B
and C. If the probability of A
solving the problem is 12 and B
not solving it is 14. The whole
probability of the problem
being solved is 63/4 then what is
the probability of solving it?
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Answer:
Probability that A is able to solve = P(A) = (1 / 2).
Probability that B is able to solve = P(B) = (3 / 4).
Probability that C is able to solve = P(C) = (1 / 4).
Probability that A is not able to solve = P(a) = 1 - P(A) = (1 / 2).
Probability that B is not able to solve = P(b) = (1 / 4).
Probability that C is not able to solve = P(c) = (3 / 4).
When A, B and C are independent events; the probability that none of them will be able to solve if all of them try independently = P(a)*P(b)*P(c) = (1 / 2)*(1 / 4)*(3 / 4) = (3 / 32).
Therefore, the probability that the problem will be solved if all of them try independently = 1 - P(a)*P(b)*P(c) = (29 / 32).
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