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# Two dice are thrown simultaneously. What is the probability that 5 will not come up on either of them?

Given:

Two dice are thrown simultaneously.

To do:

We have to find the probability that 5 will not come up on either of them.

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 5 will not come up on either of the dice, are $(1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 6),$

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

Number of outcomes, where 5 will not come up on either of the dice $=25$

Total number of favourable outcomes $=25$

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

Therefore,

Probability that 5 will not come up on either of the dice $=\frac{25}{36}$

The probability that 5 will not come up on either of the dice is $\frac{25}{36}$.

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