Question

A coin is tossed and a die is thrown. Let $A$ be the event 'Head turns up on the coin and an odd number turns up on the die' and $B$ be the event 'Tail turns up on the coin and an even number turns up on the die'. Which of the following is/are true:

• A. $n(A\cap B)=6$
• B. $n(A\cup B)=6$
• C. $n(A\cap B)=0$
• D. $n(A\cup B)=0$

Answer 1

Answer: (B), (C)

$n(A\cap B)=0$

$A:\left\{\right(H,1),(H,3),(H,5\left)\right\}$
$B:\left\{\right(T,2),(T,4),(T,6\left)\right\}$
Clearly, we have no element common from the sets $A$ and $B$.
Hence $n(A\cap B)=0$
and $(A\cup B)=\left\{\right(H,1),(H,3),(H,5),(T,2),(T,4),(T,6\left)\right\}$
Hence $n(A\cup B)=6$