List of top Mathematics Questions on Probability asked in KEAM

The 10 letters of the word STATISTICS are arranged randomly. The probability that the 10-letter arrangement starts with CAT is

A committee of 4 people is selected from the members of a school council which consists of 5 students, 4 teachers and 3 administrators. The probability that the committee has no teachers is

There are 20 boys and 5 girls in a class. Three students are selected at random. If $E$ is an event of selecting one boy and two girls, then $P(E)$ is equal to

A box contains 5 white balls, one red ball and 4 black balls. If three balls are drawn at random, then the probability of getting no red ball is

A fair die is rolled once. Which one of the following is not true?

Three fair dice are rolled simultaneously. Let a, b, c be the numbers on the top of the dice. Then the probability that \( \min(a, b, c) = 6 \) is:

In a box there are four marbles and each of them is marked with distinct number from the set \( \{1, 2, 5, 10\} \). If one marble is randomly selected four times with replacement and the number on it noted, then the probability that the sum of numbers equals 18 is:

A die is rolled once. If the die shows odd number, then the probability of getting other than \( 5 \) is

An integer is chosen from the first 100 positive integers. Probability that the chosen number is a multiple of 11 is:

An unbiased die is thrown and B is an event showing an odd number on top. Then $P(B)$ is:

Let $X = \{a,\,b\}$ and $Y = \{1,\,3,\,4,\,5\}$. A subset of $X\times Y$ is selected at random. If $A$ is an event of selecting a subset of $X\times Y$ containing exactly three elements, then $P(A) =$

Let $S = \{2,\,5,\,8,\,11,\,14,\,17,\,20,\,23\}$. Two integers $m,\,n$ are chosen one by one from $S$ with replacement. Then the probability that $mn$ is odd, is

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?