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

Given:

Two dice are thrown simultaneously. 

To do:

We have to find the probability of getting a sum less 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 less than 7 are $[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1)]$

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 less than 7 $=\frac{15}{36}$

$=\frac{5}{12}$

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

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Updated on: 10-Oct-2022

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