Question

An experiment involves rolling a pair of dice and recording the numbers that come up. Following are events recorded:
$A:$ the sum is greater than $8$
$B:2$ occurs on either die
$C:$ the sum is atleast $7$ and a multiple of $3.$
Then, which of the following is/are true:

• A. $n(B\cap C)=0$
• B. $n(A\cap C)=0$
• C. $n(A\cap C)=5$
• D. $n(A\cap B)=0$

Answer 1

Answer: (A), (C), (D)

$n(A\cap B)=0$

$A:(3,6),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6)$
$B:(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(1,2),(3,2),(4,2),(5,2),(6,2)$
$C:(3,6),(6,3),(5,4),(4,5),(6,6)$
Clearly, we do not have any common elements between $A$ and $B$. Hence, we have: $n(A\cap B)=0$
Also, $A\cap C=(3,6),(6,3),(5,4),(4,5),(6,6)$
since $C$ is a subset of $A$
Hence, $n(A\cap C)=5$
Also $n(B\cap C)=0$ since we have no common elements.