Nishit K Sinha Solutions for Chapter: X+2 Maths, Exercise 8: Practice Exercises

Three different numbers are selected at random from set $\mathrm{A}=\{1,2,3,\dots ,10\}$. The probability that the product of two of the numbers is equal to the third is:

There are $7$seats in a row. Three persons take seats at random. The probability that the middle seat is always occupied and no two persons are consecutive is:

From a group of $10$ persons consisting of $5$lawyers,$3$doctors, and $2$engineers, four persons are selected at random. The probability that the selection contains at least one of each category is:

The odds against an event are $3$ to $4$ and the odds in favour of another independent event are $2$ to $5$. What is the probability that at least one of them can occur?

There are $3$red, $3$ blue, and $3$green balls. What is the probability that out of $3$ selected balls $2$ are red?

In the horse race, the horse Exaclibur's chances of winning are $\frac{1}{6}$, the horse Noorjehan's chances are $\frac{1}{10}$, and those of the horse Bombay are $\frac{1}{8}$. If the race starts with twelve horses and only one horse wins, then what are the chances that one of these three horses will win?

If a year has $360$days and all the months with $30$ days. What is the probability that your birthday falls on a Monday and that is an even day of an even month, given that January $1$ is a Monday?

Let $\mathrm{A}$ and $\mathrm{B}$ be two independent events in such a way that their probabilities are $\frac{3}{10}$ and $\frac{2}{5}$, respectively. The probability of exactly one of the events happening is: