Probability

Urn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?

In throwing of two dice, the number of exhaustive events that '5' will never appear on any one of the dice is

In an entrance test there are multiple choice questions. There are four options for each question, of which only one is correct. The probability that a student knows the answer to a question is $90\%$. If he gets the…

If two fair dice are tossed, then what is the probability that the sum of the numbers on the faces of the dice is strictly greater than 7?

A person $X$ speaks the truth 4 out of 5 times and person $Y$ speaks the truth 5 out of 6 times. What is the probability that they will contradict each other in stating the fact?

Three boys, P, Q, R an three girls S, T, U are to be arranged in a row for a group photograph. What is the probability that Q and U sit together?

A biased coin with the probability of getting head equal to $\frac{1}{4}$ is tossed five times. What is the probability of getting tail in all the first four tosses followed by head?

In a binomial distribution, the mean is $\frac{2}{3}$ and variance is $\frac{5}{9}$. What is the probability that random variable $X=2$ ?

The incidence of suffering from a disease among workers in an industry has a chance of $33 \frac{1}{3} \%$. What is the probability that exactly 3 out of 6 workers suffer from a disease?

Let $A$ and $B$ be two independent events such that $P(\bar{A})=0.7, P(\bar{B})=k, P(A \cup B)=0.8$ What is the value of k ?

What is the probability that the month of December has 5 Sundays ?

Consider the following relations for two events $E$ and $F$ : $\begin{array}{ll} \text { 1. } & P(E \cap F) \geq P(E)+P(F)-1 \\ \text { 2. } & P(E \cup F)=P(E)+P(F)+P(E \cap F) \\ \text { 3. } & P(E \cup F) \leq…