# In a simultaneous throw of a pair of dice, find the probability of getting an even number on one and a multiple of 3 on the other.

Given:

Two dice are thrown simultaneously.

To do:

We have to find the probability of getting an even number on one and a multiple of 3 on the other.

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 an even number on one and a multiple of 3 on the other are $[(2, 3), (2, 6), (4, 3), (4, 6), (6, 3), (6, 6), (3, 2), (6, 2), (3, 4), (6, 4), (6, 6)]$

Total number of favourable outcomes $=6$

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

Therefore,

Probability of getting an even number on one and a multiple of 3 on the other $=\frac{11}{36}$

The probability of getting an even number on one and a multiple of 3 on the other is $\frac{11}{36}$.

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Updated on: 10-Oct-2022

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