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# In a simultaneous throw of a pair of dice, find the probability of getting a doublet of prime numbers.

Given:

Two dice are thrown simultaneously.

To do:

We have to find the probability of getting a doublet of prime numbers.

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 doublet of prime numbers are $[( 2,\ 2),\ ( 3,\ 3),\ ( 5,\ 5)]$

Total number of favourable outcomes $=3$

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

Therefore,

Probability of getting a doublet of prime numbers $=\frac{3}{36}$

$=\frac{1}{12}$

The probability of getting a doublet of prime numbers is $\frac{1}{12}$.

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