Question

Two dice are thrown. What is the probability that the sum of the numbers appearing on the two dice is $11,$ if $5$ appears on the first $?$

• A. $\frac{1}{36}$
• B. $\frac{1}{6}$
• C. $\frac{5}{6}$
• D. None of these

Answer 1

The correct option is B

$\frac{1}{6}$

Find the required probability:

If two dice are thrown, the total number of sample space $=36$

Let $A$ be the event that the first die contains $5,P\left(A\right)=\left\{(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)\right\}=\frac{6}{36}$

Let $B$ be the event that the sum of numbers appearing on two dice is $11,P\left(B\right)=\left\{(5,6)(6,5)\right\}$

$P(A\cap B)=\frac{1}{36}$

Hence$,P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P\left(A\right)}$

$$\begin{gathered} =\frac{\left({\displaystyle \frac{1}{36}}\right)}{\left({\displaystyle \frac{6}{36}}\right)} \\ =\frac{1}{6} \end{gathered}$$

Hence, option (B) is correct