List of top Mathematics Questions on Probability asked in KEAM

If $M$ and $N$ are events such that $P(M\cup N)=\frac{3}{4}$, $P(M\cap N)=\frac{1}{4}$, and $P(\overline{M})=\frac{2}{3}$, then $P(\overline{M}\cap N)$ is

If \( A \) and \( B \) are two events associated with an experiment such that \( P(A \cup B) = P(A \cap B) \), and \( P(A) = 1/3 \), then \( P(B) \) equals

Three identical fair dice are rolled. The probability that the same number appears on each of them is

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of red ball, the number of blue balls must be

A pair of fair dice are rolled together. The probability of getting a total of 8 is

Two dice of different colours are thrown at a time. The probability that the sum is either 7 or 11 is

Two dice of different colours are thrown at a time. The probability that the sum is either 7 or 11 is

Let \( a \) and \( b \) be 2 consecutive integers selected from the first 20 natural numbers. The probability that \( \sqrt{a^2 + b^2 + a^2b^2} \) is an odd positive integer is

An ellipse of eccentricity \( \frac{2\sqrt{2}}{3} \) is inscribed in a circle. A point is chosen inside the circle at random. The probability that the point lies outside the ellipse is

Two dice of different colours are thrown at a time. The probability that the sum is either 7 or 11 is

Let \( a \) and \( b \) be 2 consecutive integers selected from the first 20 natural numbers. The probability that \( \sqrt{a^2 + b^2 + a^2b^2} \) is an odd positive integer is

An ellipse of eccentricity \( \frac{2\sqrt{2}}{3} \) is inscribed in a circle. A point is chosen inside the circle at random. The probability that the point lies outside the ellipse is

In a class, 40% of students study maths and science and 60% of students study maths. What is the probability of a student studying science given the student is already studying maths?

Coin tossed and die rolled: probability of head and 3

Two dice of different colours are thrown at a time. The probability that the sum is either 7 or 11 is

An ellipse of eccentricity \( \frac{2\sqrt{2}}{3} \) is inscribed in a circle. A point is chosen inside the circle at random. The probability that the point lies outside the ellipse is

Let \( a \) and \( b \) be 2 consecutive integers selected from the first 20 natural numbers. The probability that \( \sqrt{a^2 + b^2 + a^2b^2} \) is an odd positive integer is

In a class, 40% of students study maths and science and 60% of students study maths. What is the probability of a student studying science given the student is already studying maths?

Three players A, B and C play a game. The probability that A, B and C will finish the game are respectively $\frac{1}{2} , \frac{1}{3}$ and $\frac{1}{4}$ . The probability that the game is finished is

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

Three unbiased coins are tossed. The probability of getting at least 2 tails is:

Let \(A\) and \(B\) be two events. Then \(1 + P(A \cap B) - P(B) - P(A)\) is equal to

Out of $15$ persons, $10$ can speak Hindi and $8$ can speak English. If two persons are chosen at random, then the probability that one person speaks Hindi only and the other speaks both Hindi and English is

If $A$ and $B$ are mutually exclusive events and if $ p(B)=\frac{1}{3},p(A\cup B)=\frac{13}{21}, $ then $P(A)$ is equal to

A die has four blank faces and two faces marked $3$. The chance of getting a total of $12$ in $5$ throws is