An integer is chosen at random from the numbers ranging from $1$ to $50$ . What is the probability that the integer chosen is a multiple of $2$ or $3$ or $10$?

A bag contains tickets numbered $1$ to $20$. Two tickets are drawn. Find the probability that

$\left(\mathrm{i}\right)$ Both the tickets have prime numbers on them.

$\left(\mathrm{ii}\right)$ On one there is a prime number and on the other there is a multiple of $4$.

A class consists of $6$ boys and $4$ girls. Three students are selected at random. What is the probability that the selected group has

$\left(\mathrm{i}\right)$ All boys?

$\left(\mathrm{ii}\right)$ Exactly $1$ boy and $2$ girls?

$\left(\mathrm{iii}\right)$ At least $2$ girls?

A bag contains 4 white, 5 red and 6 black balls, 4 balls are drawn at random. Find the probability that At least one ball of each colour is chosen

$\left(\mathrm{i}\right)$ The draw contains no black ball

$\left(\mathrm{ii}\right)$ Exactly $2$ black balls

$\left(\mathrm{iii}\right)$ All are of the same colour

$\left(\mathrm{iv}\right)$ At least one ball of each colour is chosen

$E_1$ and $E_2$ are two events of a random experiment such that $P\left(E_1\right)=0.50, P\left(E_2\right)=0.40$ and $P\left(E_1 \mathrm{and} E_2\right)=0.15$, find the probability that

$\left(\mathrm{i}\right)$ At least one of $E_1$ and $E_2$ occurs

$\left(\mathrm{ii}\right)$ Neither $E_1$ nor $E_2$ occurs

Two dice are thrown. The events $A,B,C,D$ are as follows :

$A:$ Getting an even number on the first die

$B:$ Getting an odd number on the first die

$C:$ Getting sum of numbers on two dice $\le 5$.

$D:$ Getting the sum of numbers on two dice $\le 10$.

Describe the events

$\left(\mathrm{i}\right)$ $A^{\text{'}}$

$\left(\mathrm{ii}\right)$ $A$ or $B$

$\left(\mathrm{iii}\right)$ $B$ and $C$

$\left(\mathrm{iv}\right)$ $A$ and $D$

Two dice are thrown simultaneously and three events $A,B$ and $C$ are defined as

$A:$ The sum of the numbers is $10$

$B:$ The sum of the numbers is $9$

$C:$ The sum of the numbers is $8$

If $P\left(E\right)$ is the probability of event $E$, then which of the followings is true?