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?

You are tossing a fair coin repeatedly until a ‘Head’ appears. The expected number of tosses required for a ‘Head’ to appear is ...........

Anubhab faces a multiple-choice question (MCQ) with four alternative choices, where only one is the right choice. There is no negative mark for making a wrong choice. Also, assume that the probability that he knows the answer is 0.50. The probability of making the correct choice is 0.25, if he does not know the answer. He got full marks in this question.
The probability that he knew the answer is ......... (rounded off to one decimal place).

A fair coin is tossed 3 times in succession. The probability of the event that ‘both first and second toss result in head’ is (rounded off to two decimal places).

Two cards are drawn from a full pack of 52 cards at random. The probability of getting a heart and a diamond is (rounded off to two decimal places).