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J2S2019
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IanStewart
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IanStewart
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Probability that A can solve a problem is (1/4) & Probability that B can solve the same problem is (1/2). If they start solving the same problem simultaneously, then what is the probability that the problem gets solved?

A>1/8
B>5/8
C>1/2
D>3/8
E>3/4

You can't answer the question unless you know the two probabilities are independent. As the question is worded, the answer could be anything between 1/2 and 3/4.

If you know the two probabilities are independent, then the probability A does *not* solve the problem is 3/4, the probability B does *not* solve the problem is 1/2, and the probability both do not solve the problem is thus (3/4)(1/2) = 3/8. Subtracting that from 1, we find the probability that at least one of them solves the problem is 5/8.

But we're not told the probabilities are independent. It could be true that A, who is the worse problem-solver of the two, can only solve easy problems, and B can solve both easy and medium problems. So it could be true that any time A can solve the problem, B can easily solve it. Then the problem only gets solved if B can do it, so only gets solved 1/2 the time.

Or it could be true that any time A can solve the problem, B cannot solve it -- maybe the problems are drawn from a question bank consisting of 1/4 Astronomy questions, 1/2 Art History questions, and 1/4 Archaeology questions, and A is an Astronomy expert and B is an Art History expert, and those are the only problems each can solve. In that case, 3/4 of the time one of them will solve the problem (but it will never be true that both solve it).

These kinds of questions need to be carefully worded to have any mathematical meaning. What is the source?

IanStewart, thanks for pointing this out, mistakenly over-looked the wording.
Post is now edited. :please
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Is this a problem you've designed? What's important is not that the people are solving the problem "independently"; what matters is that the two probabilities are independent of each other.
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Is this a problem you've designed? What's important is not that the people are solving the problem "independently"; what matters is that the two probabilities are independent of each other.

Yeah i have designed this one, but i have seen similar one somewhere in a Youtube channel, thought of posting it in the forum.
Hope now the question stem is somewhat clear. :|

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