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In a simultaneous throw of a pair of dice, find the probability of getting a number other than 5 on any dice.
Given:
Two dice are thrown simultaneously.
To do:
We have to find the probability of getting a number other than 5 on any dice.
Solution:
When two dice are thrown, the total possible outcomes are $6\times6=36$.
This implies,
The total number of possible outcomes $n=36$
Outcomes where we get 5 at least once are $[(1, 5), (2, 5), (3, 5), (4, 5), (6, 5), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)]$
Number of outcomes where we get 5 at least once $=11$
Number of outcomes where we get a number other than 5 on any dice $=36-11=25$
Total number of favourable outcomes $=25$
Probability of an event $=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
Therefore,
Probability of getting a number other than 5 on any dice $=\frac{25}{36}$
The probability of getting a number other than 5 on any dice is $\frac{25}{36}$.
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