Question 1096149
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The probability that A solves the problem is 0.65, so the probability that A does NOT solve the problem is {{{1-0.65 = 0.35}}}.<br>
The probability that B solves the problem is 0.75, so the probability that B does NOT solve the problem is {{{1-0.75 = 0.25}}}.<br>
Then the probability that NEITHER A NOR B solves the problem is {{{0.35*0.25 = .0875}}}<br>
And so the probability that someone solves the problem is {{{1-.0875 = 0.9125}}}.<br>
And finally the probability that A solves the problem, GIVEN THAT someone solves the problem, is {{{0.65/0.9125 = 0.71233}}} (to 5 decimal places).<br>
If you want an exact answer, use fractions instead of decimals:<br>
The probability that A solves the problem is 13/20, so the probability that A does NOT solve the problem is {{{1-13/20 = 7/20}}}.<br>
The probability that B solves the problem is 3/4, so the probability that B does NOT solve the problem is {{{1-3/4 = 1/4}}}.<br>
Then the probability that NEITHER A NOR B solves the problem is {{{(7/20)*(1/4) = 7/80}}}<br>
And so the probability that someone solves the problem is {{{1-7/80 = 73/80}}}.<br>
And finally the probability that A solves the problem, GIVEN THAT someone solves the problem, is {{{(13/20)/(73/80) = (52/80)/(73/80) = 52/73}}}.<br>