Probability Questions for CAT

What is the probability of throwing a number greater than 2 with a fair dice?

100 students appeared for two examinations. 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has failed in both the examinations?

The probability that two friends A and B have their birthdays on two consecutive days of the week is:

Three coins are tossed. What is the probability of getting three heads?

Three coins are tossed in the air. What are the chances that at least two coins land with tails facing upwards?

Three coins are tossed. What is the probability of getting neither 3 Heads nor 3 Tails?

Two students X and Y are best friends. They sit randomly in a row of 9 seats with 7 other friends. What is the probability that X and Y sit together?

What is the maximum possible sum of the number of Mondays and Thursdays in two consecutive years?

A bag contains $8$ red and $6$ blue balls. If $5$ balls are drawn at random, what is the probability that $3$ of them are red and $2$ are blue?

Ajay and Vijay have lunch at the same place for twenty minutes each between 1 pm and 2 pm every day. What is the probability that they meet on a normal day?

A bag contains 8 white and 4 red balls. Five balls are drawn at random. What is the probability that two of them are red and 3 are white?

X is the probability of having 53 Sundays in a non-leap year and Y is the probability of having 5 Sundays in February in a leap year.

Two balls are drawn from an urn one after another without replacement. If the urn contains 7 red and 8 blue balls, then find the probability of drawing blue as the second ball.

Balls divided in 2 bags such that red = 5 and white = 12. Find division to minimize red probability.

Dheeraj picks a random page number (three-digit) from a dictionary. If the sum of the first two digits equals the last digit minus 3 and also equals ⌊(last digit)/2⌋ + 1, what is the probability that the middle digit is 0?

If $P(A) = \frac{3}{7},\ P(B) = \frac{1}{2}$ and $P(A' \cap B') = \frac{1}{14}$, then are A and B mutually exclusive?

Set A consists of 15 odd and 15 even natural numbers, with no two sums being equal. Set B contains the sums of all pairs from Set A. If a number is randomly selected from Set B, and the probability that the number is odd is expressed as a/b (in simplest form), what is the value of a+b?

Rajesh passes in Math, Physics and Chemistry with probabilities $m$, $p$ and $c$. It is given that: - P(at least one subject) = 0.75 - P(at least two subjects) = 0.5 - P(exactly two subjects) = 0.4 Find the value of $p + m + c$.

A locker at the RBI building can be opened by dialling a fixed three-digit code (between 000 and 999). Chhota Chetan, a terrorist, only knows that the number is a three-digit number and has exactly one digit '6'. Using this information, he tries to open the locker by dialling three digits at random. What is the probability that he succeeds?

$A$ and $B$ throw one dice for a stake of ₹11, which is to be won by the player who first throws a six. The game ends when the stake is won by $A$ or $B$. If $A$ has the first throw, what are their respective expectations?