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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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