Question

Two dice $A$ and $B$ are rolled. If it is known that the number on $B$ is $5$, then the probability that the sum of the numbers on the two dice will be greater than $9$ is

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

Answer 1

Answer: (A)

Consider the events
$A=$ Sum of number in two dice be greater than 9
$B=$ Number of dice $B$ is 5
$\therefore P(A)=\frac{6}{36}$
$P(B)=\frac{6}{36}$
$P(A\cap B)=\frac{2}{36}$
Required probability $=P\left(\frac{A}{B}\right)=\frac{P(A\cap B)}{P(B)}=\frac{2}{6}=\frac{1}{3}$