A dice is rolled twice. Find the probability that 5 will come up exactly one time.

Given:

A dice is rolled twice.

To do:

We have to find the probability that 5 will come up exactly one time.

Solution:

When a die is rolled twice, the total possible outcomes are $6\times6=36$.

This implies,

The total number of possible outcomes $n=36$

Outcomes, where 5 will come up exactly one time, are $(1, 5), (2, 5), (3, 5), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4), (5, 6), (6, 5)$

Number of outcomes, where 5 will come up exactly one time $=10$

Total number of favourable outcomes $=10$

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

Therefore,

Probability that 5 will come up exactly one time $=\frac{10}{36}$

$=\frac{5}{18}$

The probability that 5 will come up exactly one time is $\frac{5}{18}$.       

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Updated on: 10-Oct-2022

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