A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability that of obtaining the same number on both dice?

Given:

A black die and a white die are thrown at the same time.

To do:

We have to write all the possible outcomes and find the probability that of obtaining the same number on both dice.

Solution:

When two dice are thrown, the total possible outcomes are $6\times6=36$.

All the possible outcomes are $(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4),$

$(2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1),$

$(5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)$

This implies,

The total number of possible outcomes $n=36$

Outcomes, where we obtain the same number on both dice, are $[(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)]$

Total number of favourable outcomes $=6$

Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$

Therefore,

Probability of obtaining the same number on both dice $=\frac{6}{36}$

$=\frac{1}{6}$

The probability of obtaining the same number on both dice is $\frac{1}{6}$.