Question

Two dice are thrown simultaneously. Find the probability of getting prime number on each dice.

Answer 1

Step 1: Find the number of favourable outcomes:

Sample space for throwing two dice will be,

$$\begin{gathered} n\left(S\right)={\text{(number of possible outcomes of throwing a dice)}}^{\text{number of dices thrown}} \\ n\left(S\right)={\left(6\right)}^2 \\ n\left(S\right)=36 \end{gathered}$$

The prime number on one dice will be $\{2,3,5\}$.

Thus, the favourable outcomes will be,

$=(2,2),(2,3),(2,5),(3,2),(3,3),(3,5),(5,2),(5,3),(5,5)$

Therefore, the number of favourable outcomes will be $9$.

Step 2: Use the formula for probability:

$\text{Probability =}\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Thus, the probability will be,

$$\begin{gathered} \text{Probability=}\frac{9}{36} \\ \mathrm{Probability}\text{=}\frac{1}{4} \end{gathered}$$

Final answer:

Hence, the probability of getting a prime number on each dice is $\frac{1}{4}$.