List of top Mathematics Questions on Probability asked in IIT JAM EN

The chance of rain on a day when an outdoor picnic is arranged is \(40\%\). If it rains, the chance that the picnic will be ‘good and enjoyable’ is \(30\%\). However, if it does not rain, the chance that the picnic will be ‘good and enjoyable’ is \(80\%\). The chance (in %) that it was raining on the day of picnic, given that the picnic was indeed ‘good and enjoyable’ is (in integer).

It is given that \(\text{Prob}(-1 \leq z \leq 1)=0.683\), \(\text{Prob}(-2 \leq z \leq 2)=0.954\), and \(\text{Prob}(-3 \leq z \leq 3)=0.997\), when \(z\) follows a standard normal distribution. If \(X\) follows a normal distribution with mean and variance as \(5\) and \(4\), respectively, then \(\text{Prob}(1 \leq X \leq 7)=\underline{}\) (rounded off to three decimal places).

In a year of \(366\) days, what is the chance that three persons have different birthdays?