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If the probability of solving a problem by two students George and James are 1/2 and 1/3 respectively then what is the probability of the problem to be solved.

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Let A and B be the probabilities of solving the problem by George and James respectively.
Then P(A)=1/2 and P(B)=1/3.
The problem will be solved if it is solved at least by one of them also.
So, we need to find P(AUB).
By addition theorem on probability, we have
P(AUB) = P(A) + P(B)- P(A∩B).
P(AUB) = 1/2 +.1/3 – 1/2 * 1/3 = 1/2 +1/3-1/6 = (3+2-1)/6 = 4/6 = 2/3


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