Question

A coin is tossed and a die is thrown simultaneously :
$P$ is the event of getting head and a odd number.
$Q$ is the event of getting either $H$ or $T$ and an even number.
$R$ is the event of getting a number on die greater than $7$ and a tail.

$S$ is the sample space.

Which of the following options is correct?

• A. $n\left(S\right)=12,n\left(P\right)=3,n\left(Q\right)=2,n\left(R\right)=0$
• B. $n\left(S\right)=12,n\left(P\right)=3,n\left(Q\right)=3,n\left(R\right)=0$
• C. $n\left(S\right)=12,n\left(P\right)=3,n\left(Q\right)=6,n\left(R\right)=0$
• D. $n\left(S\right)=12,n\left(P\right)=3,n\left(Q\right)=5,n\left(R\right)=0$

Answer 1

Answer: (C)

$n\left(S\right)=12,n\left(P\right)=3,n\left(Q\right)=6,n\left(R\right)=0$

A coin is tossed and a die is thrown simultaneously.

$S=\{H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6\}$

Thus $n\left(S\right)=12$

$P$ is the event of getting head and an odd number.

$P=\{H1,H3,H5\}$

Thus $n\left(P\right)=3$

$Q$ is the event of getting either $H$ or $T$ and an even number.

$Q=\{H2,H4,H6,T2,T4,T6\}$

Thus $n\left(Q\right)=6$

$R$ is the event of getting a number greater than $7$ and tail $1$.

$R=\left\{\right\}$

$\therefore n\left(R\right)=0$

Hence, option C is correct.