Probability

In a building, an elevator starts from the ground floor (that is, 0th floor) with $10$ passengers and stops at every floor until the 15th floor which is the topmost floor. No new passengers enter the elevator on any…

The probability that the sum of two integers $m$ and $n$, where $m, n \in \{1, 2, \ldots, 50\}$, chosen randomly and independently, being divisible by $3$ is

Amar, Akbar, and Anthony write a test independently. The probability that Amar passes the test and Akbar fails the test is $\dfrac{3}{20}$. The probability that Akbar passes the test and Anthony fails the test is…

Let $X$ and $Y$ be two students who have appeared NEST. Given that i. the probability that X qualifies NEST is $\frac{1}{10}$; ii. the probability that X qualifies NEST given that Y qualifies NEST is $\frac{1}{2}$; iii.…

Let $k, l$ and $m$ be three 3 -digit numbers chosen randomly. Then the probability that $k+l+m$ is divisible by number 3 is

The sports club in a university changes its president every semester. Last year, the president for the first semester was chosen randomly from a collection of 80 students (boys and girls), out of whom 48 are boys. The…

A man has two homes - one in city A and another in city B . He travels between these two cities by flights. The only flight from city A to city B is scheduled at 6:00 AM every day and the only flight from city B to city…

If a teacher assigns homework on the $n$th day, the probability that she will assign homework on the $(n+1)$ th day is $\frac{1}{3}$. If she does not assign homework on the $n$th day, the probability that she will…

In a throw of a (biased single) dice, the probability of the outcome being a number $n$ is $\frac{1}{4}$ if $n$ is even, and $\frac{1}{12}$ if $n$ is odd. If the dice is thrown twice, then the probability that the sum…

The probabilities of getting a head for one coin is $\frac{1}{4}$ and for an another coin is $\frac{2}{3}$. If both the coins are tossed simultaneously, then the probability of getting a head and a tail is

Class XI has 4 boys and 6 girls, and Class XII has 4 boys and 3 girls. One student is selected at random from one of the classes (either class being equally likely). The selected student is a girl. The probability that…

Let A, B and C be three events with non-zero probabilities. Then