When two dice are thrown simultaneously What is the probability of obtaining the same number on both dice?

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Let A be the event of getting same number on both dice.

Elementary events favourable to event A are (1,1),(2,2)(3,3),(4,4),(5,5) and (6,6). Favourable number of outcomes = 6

$∴ P (A) = \frac{6}{36} = \frac{1}{6}$

So, required probability is

\frac{1}{6}

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Text Solution

Answer : C

Solution : Total number of all possible outcomes = 36. <br> Getting same number on both dice means getting <br> (1,1),(2,2),(3,3),(4,4),(5,5),(6,6). <br> Their number is 6. <br> `:. ` P(getting the same number on both dice) =`6/36 = 1/6`.

If two identical dice are thrown simultaneously (The order of result does not matter. For example, $(2, 3)$ and $(3, 2)$ are considered same), what is the probability of getting same number on both the dice?

My attempt:
Now the reduced sample space is of size = $6+{6 \choose 2} = 6 + 15 = 21$.

Though the sample space is reduced from $36$ to $21$, the probability of getting the same number on both dice is $\frac{1}{36}$, and the probability of getting different number on both the dice is $\frac{2}{36}$.

Since we have $6$ possibilities of getting same number on both the dice, the required probability is $\frac{6}{36} = \frac{1}{6}$