Probability Questions with Solutions

In a tuition batch of two students, the probability that $X$ will pass the exam is $\frac{2}{5}$ and that of $Y$ is $\frac{3}{4}$. What is the probability that neither of $X$ and $Y$ will pass the exam? Assume that the outcomes of exams for $X$ and $Y$ are independent of each other.

Let $A_1,A_2,A_3$ be three events in a sample space with the condition $A_1\cap A_2\ne \varphi$. Then always:

A die is rolled twice independently. What is the probability that either the first die shows a number no less than 4 or the second die shows at least 4?

Find the probability of guessing correctly at least six of 10 answers in a True or False objective test.

Two customers, Rachana and Bhakti, are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on consecutive days?

Two customers, Rachana and Bhakti, are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on consecutive days?

A bookshelf has 5 red books, 3 blue books, and 4 green books. If you randomly select a book from the shelf, what is the probability that it is blue?

Two numbers are selected randomly from a set $S=1,2,3,4,5,6$ without replacement one by one. The probability that minimum of the two numbers is less than 4 is :

The probability of a shooter hitting a target is $\frac{3}{4}$. How many minimum numbers of times must he/she fire so that the probability of hitting the target at least once is more than 0.99?

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 values for the probability of event B are given by

A bag contains 5 yellow, 4 black and 3 green balls. If 3 balls are drawn at random, find the probability that no black ball is chosen.

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. Then the probability that the transferred ball is red is

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 the total computers produced. 7% of the computers produced in the factory turn out to be defective. It is known that P(computer turns out to be defective given that it is produced in plant $T_1$) = 10 P(computer turns out to be defective given that it is produced in plant $T_2$). 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

A speaks the truth in 60% of cases and B in 50% of cases. In what fraction of cases are they likely to contradict each other while narrating the same incident?

A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is

Person A can hit a target 4 times in 5 attempts, person B 3 times in 4 attempts and person C 2 times in 3 attempts. They fire a volley. The probability that the target is hit at least two times is

Atal speaks the truth in 70% and George speaks the truth in 60% of cases. In what percentage of cases are they likely to contradict each other in stating the same fact?

If A and B are two events such that $P\left(A\cup B\right)=\frac{5}{6}$, $P\left(A\cap B\right)=\frac{1}{3}$ and $P\left(\overline{B}\right)=\frac{1}{2}$, then the events A and B are

Two fair dice are tossed. What is the probability that the total score is a prime number?

A determinant is chosen at random from the set of all determinants of matrices of order 2 with elements 0 and 1 only. The probability that the determinant chosen is non-zero is