List of top Mathematics Questions on Probability asked in NIMCET

In a tuition batch of 2 students, the probability that \(X\) will pass the examination is \(\frac25\) and that of \(Y\) is \(\frac34\). Assuming independence, what is the probability that neither \(X\) nor \(Y\) will pass?

Let \(A_1,A_2,A_3\) be events in a sample space with \(A_1\cap A_2\neq \phi\). Then always:

A die is rolled twice independently. Probability that either first die shows number no less than \(4\) or second die shows at least \(4\)?