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)

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