Q77 / 120 · VITEEE 2006 · Mathematics
In rolling two fair dice, what is the probability of obtaining a sum greater than 3 but not exceeding $6 ?$
- A$\frac{1}{2}$
- Correct answerB$\frac{1}{3}$
- C$\frac{1}{4}$
- D$\frac{1}{6}$
Solution
Let $S$ be the sample space
$\because \mathrm{n}(\mathrm{S})=36$
Events
[sum greater than 3 but not exceeding 6]
$\begin{array}{l}
=\{(2,2),(3,1),(1,3),(4,1),(1,4),(5,1)(1,5) \\
(3,2),(2,3),(4,2),(2,4),(3,3)\} \\
\Rightarrow \mathrm{n}(\mathrm{E})=12 \\
\therefore \text { Required probability }=\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}=\frac{12}{36}=\frac{1}{3}
\end{array}$
Hence, the correct answer is option: 'B'.