Two dice are thrown independently. Let A be the event that the number appeared on the 1^st die is less than th…

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 $2^{\text{nd}}$ die is odd, and $C$ be the event that the number appeared on the $1^{\text{st}}$ die is odd and that on the $2^{\text{nd}}$ die is even. Then:

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

Accepted Answer

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

Answer

B. $$ A $$ and $$ B $$ are mutually exclusive.

Answer

C. The number of favourable cases of the events $$ A, B, $$ and $$ C $$ are $$15, 6, $$ and $$6$$ respectively.

Answer

D. $$ B $$ and $$ C $$ are independent.

Answer & step-by-step solution

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