​A dice is thrown twice and the sum of the appearing numbers is 10. Then the probability that the number 5 has appeared at least once is: ​

Correct option is B

Given:

A die is thrown twice, and the sum of the appearing numbers is 10.

We need to find the probability that the number 5 appeared at least once.

Formula Used:

The total number of outcomes when a die is thrown twice is $6\times 6=36$.

The probability of an event is given by:

​$$P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$​​

Solution:

Find the possible outcomes where the sum is 10

The possible pairs of numbers that sum to 10 are:

(4, 6), (5, 5), (6, 4)

So, the total number of outcomes where the sum is 10 is 3.

Find the outcomes where the number 5 appears at least once

The only pair that includes the number 5 is (5, 5).

So, the number of favorable outcomes where 5 appears at least once is 1.

​$$P(\text{5 appears at least once}) = \frac{1}{3}$$

Option (B) is right answer.

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