Probability PYQs - Last 10 Years

A number \(\mathrm{n}\) is chosen at random from \(s=\{1,2,3, \ldots, 50\}\). Let \(\mathrm{A}=\{n \in s: n\) is a square \(\}\), \(\mathrm{B}=\{n \in s: n\) is a prime\(\}\) and \(\mathrm{C}=\{n \in s: n\) is a square\(\}\). Then, correct ...

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answer just by guessing, is

If A, B and C are three mutually exclusive and exhaustive events such that P(A) = 2P(B) = 3P(C). What is P(B)?

Three vertices are chosen randomly from the seven vertices of a regular 7-sided polygon. The probability that they form the vertices of an isosceles triangle is

If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fail is

Five persons A, B, C, D and E are in queue of a shop. The probability that A and B are always together is

The probability of choosing randomly a number c from the set {1, 2, 3, ... 9} such that the quadratic equation \(x^2+4x+c=0\) has real roots, is

A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that he knows the correct answer is \(p,0 < p < 1\). If he does not know the correct answer, he randomly ticks one answer. Gi...

If A, B and C are mutually exclusive and exhaustive events of a random experiment such that \(P(B) = {3 \over 2}P(A)\) and \(P(C) = {1 \over 2}P(B)\), then \(P(A \cup C)\) equals

Five persons A, B, C, D and E are in queue of a shop. The probability that A and E are always together, is

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral equals

The coefficients a, b and c of the quadratic equation, \(ax^2+bx+c=0\) are obtained by throwing a dice three times. The probability that this equation has equal roots is