DFG5150 wrote:

Why the answer doesn't make much sense to me??

I strongly believe that since the probability of Mike or Rob winning, conditional on Ben losing, is 7/12, then that means that:

7/12=(1-1/7)*(x+y), where x and y are the probabilities of Mike or Rob winning respectivelly. That would mean x+y=49/72.

The OE says that x+y=(1-1/7)*7/12...

I am not sure I get what you mean. here is a copy of the OE just in case - which part do you disagree with?

The probability of Mike or Rob winning, conditional on Ben losing, is \(\frac{1}{4} + \frac{1}{3}\) or \(\frac{7}{12}\) . The unconditional probability (to take into consideration the probability of Ben winning) is then \((1-\frac{1}{7}) * \frac{7}{12} = \frac{6}{7} * \frac{7}{12} = \frac{1}{2}\) .

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