Odisha Board Solutions for Chapter: Probability, Exercise 1: EXERCISES 16 (a)

A die is rolled three times. Find the probability that the numbers obtained are in strictly increasing order. Write the final answer in simplest form of fraction.

Three phono records are removed from their jackets, played and then returned to the jackets at random. Find the probability that none of the records goes to the right jacket. (Express your answer as the simplest form of fraction)

Three phono records are removed from their jackets, played and then returned to the jackets at random. Find the probability that just one record goes to the right jacket.

Three phono records are removed from their jackets, played and then returned to the jackets at random. Find the probability in fractional form that none of the records goes to the right jacket.

Four records are taken out of their jackets, played and returned to the jackets at random. Find the probability that none of the records goes into the right jacket.

Four records are taken out of their jackets, played and returned to the jackets at random. Find the probability that atleast one record is put in the right jacket. (Express your answer as the simplest form of fraction)

Let $\mathrm{A}$ and $\mathrm{B}$ be events with $\mathrm{P}\left(\mathrm{A}\right)=\frac{1}{3}, \mathrm{P}\left(\mathrm{A}\cup \mathrm{B}\right)=\frac{3}{4}$ and $\mathrm{P}\left(\mathrm{A}\cap \mathrm{B}\right)=\frac{1}{4}.$ Find $\mathrm{P}\left({\mathrm{A}}^{\text{'}}\right)$.

A committee of $3$ is to be chosen from among $10$ people including $X$ and $Y$. Find the probability that $X$ is in the committee