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 \(4\)?

Consider the sample space \( \Omega = \{(x, y): x, y \in \{1, 2, 3, 4\} \} \) where each outcome is equally likely. Let \( A = \{ x \geq 2 \} \) and \( B = \{ y > x \} \) be two events. Then which of the following is NOT true?

Let E and F be two events such that \( P(E) > 0 \) and \( P(F) > 0 \). Which one of the following is NOT equivalent to the condition that \( P(E) = P(E \cap F) \)?

Bag I contains 3 red, 4 black, and 3 white balls and Bag II contains 2 red, 5 black, and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball drawn is found to be black in colour. Then the probability that the transferred ball is red, is:

A bag contains different kinds of balls in which there are 5 yellow, 4 black, and 3 green balls. If 3 balls are drawn at random, then find the probability that no black ball is chosen.

A computer producing factory has only two plants \(T_1\) and \(T_2\). Plant \(T_1\) produces 20% and plant \(T_2\) produces 80% of total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that \( P(\text{computer turns out to be defective given that it is produced in plant } T_1) = 10P(\text{computer turns out to be defective given that it is produced in plant } T_2)\), where \( P(E) \) denotes the probability of an event \(E\). A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant \(T_2\) is

Given two events \( A \) and \( B \) such that the odds in favour of \( A \) are 2:1 and the odds in favour of \( A \cup B \) are 3:1. Consistent with this information, the smallest and largest value for the probability of event \( B \) are given by