Student has a probality to pass in english is 60% , and probality to pass in english and maths is 54% , what is probality he will fail in maths

Answer 1

Say the probability he'll pass English is Prob(E) = 0.6. The probability he'll pass in both English and Maths is Prob(E&M) = 0.54. Provided the probability that he'll pass English is independent of the probability that he'll pass Maths (and note that's an assumption we're making that may or may not be true), then the probability that he'll pass Maths must be Prob(M) = Prob(E&M) / Prob(E) = 0.54/0.6 = 0.9, because Prob(E&M) = Prob(E) x Prob(M) if the events are independent. So Prob(M) = 0.9. But we were asked for the probability that he'll fail Maths, not pass it, and that's 1 - Prob(M). So the answer must be 1 - 0.9 = 0.1. Do you agree?