In a simultaneous throw of a pair of dice, find the probability of getting a sum more than 7.

Given:

Two dice are thrown simultaneously. 

To do:

We have to find the probability of getting a sum more than 7.

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 a sum more than 7 are $[(2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)]$

Total number of favourable outcomes $=15$

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

Therefore,

Probability of getting a sum more than 7 $=\frac{15}{36}$

$=\frac{5}{12}$

The probability of getting a sum more than 7 is $\frac{5}{12}$.     

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Updated on: 10-Oct-2022

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