Question

Two dice are thrown independently. Let $A$ be the event that the number appeared on the $1^{\text {st }}$ die is less than the number appeared on the $2^{\text {nd }}$ die, $B$ be the event that the number appeared on the $1^{\text {st }}$ die is even and that on the second die is odd, and $C$ be the event that the number appeared on the $1^{\text {st }}$ die is odd and that on the $2^{\text {nd }}$ is even. Then :

• A. A and B are mutually exclusive
• B. the number of favourable cases of the events $A , B$ and $C$ are 15, 6 and 6 respectively
• C. $B$ and $C$ are independent
• D. the number of favourable cases of the event $( A \cup B ) \cap C$ is 6

Answer 1

Answer: (D)

$ \text { A : no. on } 1^{\text {st }} \text { die }<\text { no. on } 2^{\text {nd }} \text { die } $
$ \text { A : no. on } 1^{\text {st }} \text { die }=\text { even } \& \text { no. of } 2^{\text {nd }} \text { die }=\text { odd } $
$ C: \text { no. on } 1^{\text {st }} \text { die }=\text { odd } \& \text { no. on } 2^{\text {nd }} \text { die }=\text { even }$
$ n(A)=5+4+3+2+1=15 $
$n ( B )=9 $
$ n ( C )=9 $
$ n (( A \cup B ) \cap C )=( A \cap C ) \cup( B \cap C ) $
$ =(3+2+1)+0=6$