Probability Questions with Solutions

63 questions26 easy31 medium6 hard

Probability measures how likely an event is, as a number between 0 and 1. It equals the number of favourable outcomes divided by the total number of possible outcomes, when all outcomes are equally likely. This topic covers coins, dice, playing cards, drawing balls from a bag, complementary events, independent events, and conditional probability. The most useful tools are the complement rule (P(at least one) = 1 - P(none)) and the multiplication rule for independent events. For engineering and MCA entrance exams, the topic also includes the addition theorem, conditional probability, Bayes' theorem, and probability distributions. A clear sample space is the key to avoiding mistakes, so always list or count all outcomes carefully. Practise the probability questions below. Each comes with a step-by-step solution that shows how the sample space and favourable outcomes are counted.

All Questions Easy Medium Hard

Q1.
India plays 4 matches. In each match the probabilities of scoring $0$ , $1$ and $2$ points are $0.45$ , $0.05$ and $0.50$ respectively. The probability of scoring at least $7$ points is
A. $0.8750$ B. $0.0875$ C. $0.0625$ D. $0.0250$
hardAsked in NIMCET 2010View solution ›
Q2.
The probability that a man who is 85 years old will die before attaining the age of 90 is $\frac{1}{3}$ . $A_{1}, A_{2}, A_{3}, A_{4}$ are four persons aged 85 years. The probability that $A_{1}$ will die before attaining 90 and will be the first to die is:
A. $\frac{3}{5}$ B. $\frac{13}{81}$ C. $\frac{65}{324}$ D. $\frac{13}{108}$
hardAsked in NIMCET 2009View solution ›
Q3.
A bag contains $6$ red and $4$ green balls. A fair die is rolled and a number of balls equal to that appearing on the die is chosen from the bag at random. The probability that all the balls selected are red is
A. $\frac{1}{3}$ B. $\frac{3}{10}$ C. $\frac{1}{8}$ D. None of these
hardAsked in NIMCET 2008View solution ›
Q4.
The probability that a man who is $x$ years old will die in a year is $p$ . Then, amongst $n$ persons $A_{1}, A_{2}, \dots, A_{n}$ , each $x$ years old now, the probability that $A_{1}$ will die in one year and be the first to die is
A. $\frac{1}{n ^{2}}$ B. $1 - (1 - p)^{n}$ C. $\frac{1}{n ^{2}} [1 - (1 - p)^{n}]$ D. $\frac{1}{n} [1 - (1 - p)^{n}]$
hardAsked in NIMCET 2021View solution ›
Q5.
Out of $2 n + 1$ tickets, which are consecutively numbered, three are drawn at random. Then the probability that the numbers on them are in arithmetic progression is
A. $\frac{n ^{2}}{4 n ^{2} - 1}$ B. $\frac{n}{4 n ^{2} - 1}$ C. $\frac{3 n}{4 n ^{2} - 1}$ D. $\frac{3 n ^{2}}{4 n ^{2} - 1}$
hardAsked in NIMCET 2015View solution ›
Q6.
Three numbers a, b and c are chosen at random (without replacement) from among the numbers 1, 2, 3, ..., 99. The probability that $a^{3} + b^{3} + c^{3} - 3 ab c$ is divisible by 3 is
A. $\frac{3 \cdot ^{33} C _{3} + ( ^{33} C _{1} ) ^{3}}{ ^{99} C _{3}}$ B. $\frac{3 \cdot ^{33} C _{3} - ( ^{33} C _{1} ) ^{3}}{ ^{99} C _{3}}$ C. $\frac{2 \cdot ^{33} C _{3} + ( ^{33} C _{1} ) ^{3}}{ ^{99} C _{3}}$ D. $\frac{2 \cdot ^{33} C _{3} - ( ^{33} C _{1} ) ^{3}}{ ^{99} C _{3}}$
hardAsked in NIMCET 2018View solution ›