Question

A six faced unbiased die is thrown twice and 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 $\frac{1}{3}$

Given that sum of numbers appeared on upper surface is $7$. So, Set of numbers that have appeared on the upper surface are $(1,6),(6,1),(2,5),(5,2),(3,4),(4,3)$.
Out of these only two have at least one $3$
So, Probability $=\frac{2}{6}=\frac{1}{3}$