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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 $\frac{1}{6}$.