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Q.
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
TS EAMCET 2019
Solution:
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 $=P\left(\frac{A}{B}\right)=\frac{P(A \cap B)}{P(B)}=\frac{2}{6}=\frac{1}{3}$