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)

the number of favourable cases of the event $( A \cup B ) \cap C$ is 6

Answer 2

A : no. on 1st die < no. on 2nd die
A : no. on 1st die = even & no. of 2nd die = odd
C: no. on 1st die = odd & no. on 2nd die = even
n(A)=5+4+3+2+1=15
n(B)=9
n(C)=9
n((A∪B)∩C)=(A∩C)∪(B∩C)
=(3+2+1)+0=6