Question

A six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be $7$. The probability that the number $3$ has appeared at least once, is

• A. $\frac{1}{5}$
• B. $\frac{1}{2}$
• C. $\frac{1}{3}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C

$\frac{1}{3}$

Explanation for the correct option:

Step 1. Total Set of numbers appearing on the upper face of die with the sum of $7$$=\left\{(1,6),(6,1),(2,5),(2,5),(5,2),(3,4),(4,3)\right\}$

$=6$

Step 2. Outcomes of getting 3 at least once

$=\left\{(3,4),(4,3)\right\}$

$=2$

Therefore, the required probability is

$=\frac{2}{6}$

$=\frac{\mathbf{1}}{\mathbf{3}}$

Hence, Option ‘C’ is Correct.