Question

When a die is thrown, find the probabilities of (i) a prime number (ii) a number greater than $4$.

Answer 1

Part (1):- when a die is thrown, then Sample space $S=\{1,2,3,4,5,6\}$

Then, $n\left(S\right)=6$

Again we know that, Prime number between $1$ to $6$ are $2,3$ and $5$

Let $A$ be the event of prime number

Then,$n\left(A\right)=3$

Hence, Probability of prime number is$=\frac{n\left(A\right)}{n\left(S\right)}=\frac{3}{6}=\frac{1}{2}$.

Part 2:- A number greater than $4$,

Then, number greater than$4$ are $5,6$

Let $B$ be the event that greater than $4$

$B=\{5,6\}$

Then, $n\left(B\right)=2$

Hence, Probability of number greater than $4$ $=\frac{n\left(B\right)}{n\left(S\right)}=\frac{2}{6}=\frac{1}{3}$.