Probability Questions with Solutions

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?

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

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 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

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

The coefficients $a$, $b$, $c$ of $a{x}^2+bx+c=0$ are chosen by tossing 3 fair coins, where a head means 1 and a tail means 2. The probability that the roots are imaginary is

A and B throw a die in succession to win a bet with A starting first. Whoever throws 1 first wins Rs. 110. What are the respective expectations of A and B?

A and B are independent witnesses. The probability that A speaks the truth is $x$ and the probability that B speaks the truth is $y$. If both agree on a statement, the probability that the statement is true is:

If $A$ and $B$ are two events such that $P\left(A\prime \right)=0.3$, $P\left(B\right)=0.5$ and $P\left(A\cap B\right)=0.3$, then $P\left(B\mid A\cup B\prime \right)$ is

A pair of unbiased dice is rolled together till a sum of either $5$ or $7$ is obtained. The probability that $5$ comes before $7$ is

A letter is taken at random from the letters of the word STATISTICS and another letter is taken at random from the letters of the word ASSISTANT. The probability that they are the same letter is

A letter is known to have come from either TATANAGAR or CALCUTTA. On the envelope, just two consecutive letters, TA, are visible. The probability that the letter has come from CALCUTTA is

A problem in Mathematics is given to 3 students A, B and C. If the probability of A solving the problem is $\frac{1}{2}$ and B not solving it is $\frac{1}{4}$. The whole probability of the problem being solved is $\frac{63}{64}$, then what is the probability of solving it by C?

If $0<P\left(A\right)<1$, $0<P\left(B\right)<1$ and $P\left(A\cap B\right)=P\left(A\right)P\left(B\right)$, then