Question

Two dice are thrown at same time. Find the probability of getting a same number on both dice and different numbers on both dice.

Answer 1

Step 1: Find the probability of getting a same number on both dice.

We know that when two dice are thrown at same time, total number of outcomes are $36$.

To get same number on same dice, possible outcomes are $\left(1,1\right),\left(2,2\right),\left(3,3\right),\left(4,4\right),\left(5,5\right),\left(6,6\right)$

So, number of possible outcomes $=6$

As probability is the ratio of number of possible outcome and total number of outcomes.

Therefore, the probability of getting a same number on both dice $=\frac{6}{36}$

$=\frac{1}{6}$

Step 2: Find the probability of getting different numbers on both dice.

Number of possible outcomes to get different numbers on both the dice $=$Total number of outcomes $-$ Possible number of outcomes to get the same number on both the dice.

$=36-6$

$=30$

Therefore, the probability of getting different numbers on both dice $=\frac{30}{36}$

$=\frac{5}{6}$

Hence, the probability of getting a same number on both dice and different numbers on both dice are $\frac{1}{6}$ and $\frac{5}{6}$, respectively.