Question

There are $3$ men and $2$ women. a 'Gramswachhatta Abhiyan' committee of two is to be formed :
$P$ is event that the committee should contain at least one woman.
$Q$ is event that the committee should contain one man and one women.
$R$ is the event there should not be a women in the committee.

$S$ is the sample space.

Which of the following options is correct?

• A. $n\left(S\right)=10,n\left(P\right)=7,n\left(Q\right)=1,n\left(R\right)=3$
• B. $n\left(S\right)=10,n\left(P\right)=7,n\left(Q\right)=3,n\left(R\right)=3$
• C. $n\left(S\right)=10,n\left(P\right)=7,n\left(Q\right)=2,n\left(R\right)=3$
• D. $n\left(S\right)=10,n\left(P\right)=7,n\left(Q\right)=6,n\left(R\right)=3$

Answer 1

The correct option is D $n\left(S\right)=10,n\left(P\right)=7,n\left(Q\right)=6,n\left(R\right)=3$

$n\left(S\right)=10,n\left(P\right)=7,n\left(Q\right)=6,n\left(R\right)=3$
$P$ and $R$ are complementary, mutually exclusive events and exhaustive events.
$Q$ and $R$ are complementary and mutually exclusive events.