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Question

The odds against A solving a certain problem are 4 to 3, and the odds in favour of B solving the same problem are 7 to 5: what is the chane that the problem will be solved if they both try?

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Solution

Let the two events be EA and EB
Odds against favour of one A are 4:3
odds in favour of A are 3:4
probability that a solves the problem =P(EA)=37
probaility that A does not solve the problem =P(_EA)=137=47
Odds in favour of B are 7:5
probability that B solves the problem =P(EB)=712
probability that B does not solve the problem =P(_EB)=1712=512
Probability that problem is solved =P(E)=1none of them solves the problem
P(E)=1P(_EA)P(_EB)P(E)=147×512=6484

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