Question

Let three dice be thrown once. A, B and C three events are defined as
A : Sum on the dice is divisible by 6.
B : Sum on the dice has maximum number of divisors.
C : Sum on two of the dice is 11 or more
The value of $P \left(\frac{ B \cap C }{ A }\right)$ is equal to

• A. $\frac{1}{36}$
• B. $\frac{5}{36}$
• C. $\frac{6}{36}$
• D. $\frac{7}{36}$

Answer 1

Answer: (D)

A : sum on dice is 6, 12, 18
B : sum on dice is 12, 18
(12 and 18 has maximum number of divisors)
C : sum on two of the dice is 11 or more
$\therefore$ It is $12,13, \ldots \ldots 18$.

$P \left(\frac{ B \cap C }{ A }\right)=\frac{ P ( B \cap C \cap A )}{ P ( A )} $
$=\frac{ P (\text { sum } 12 \text { or } 18 \text { when two of the dice have sum } 11 \text { or more })}{ P (6 \text { or } 12 \text { or } 18)}=\frac{7}{36}$
$12 \Rightarrow 5,6,1 \rightarrow(6 \text { cases }) $
$18 \Rightarrow 6,6,6 \rightarrow \text { (1 cases). } $