The faces of a red cube and a yellow cube are numbered from 1 to 6. Both cubes are rolled. What is the probability that the top face of each cube will have the same number?

Given:

The faces of a red cube and a yellow cube are numbered from 1 to 6. Both cubes are rolled.

To do:

We have to find the probability that the top face of each cube will have the same number.

Solution:

When two cubes are rolled, the total number of possible outcomes $=6\times6=36$

This implies,

The total number of possible outcomes $n=36$.

Outcomes, where we get the same number on each die, are $[(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)]$

Total number of favourable outcomes $=6$.

We know that,

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

Therefore,

Probability that the top face of each cube will have the same number $=\frac{6}{36}$

$=\frac{1}{6}$

The probability that the top face of each cube will have the same number is $\frac{1}{6}$.     

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Updated on: 10-Oct-2022

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