# 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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Updated on: 10-Oct-2022

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