Question

Three coins are tossed simultaneously:
$P$ is the event of getting at least two heads.
$Q$ is the event of getting no heads.
$R$ is the event of getting heads on second coin.
Which of the following pairs is mutually exclusive ?

• A. $Q,R$
• B. $Q,P$
• C. $P,R$
• D. None of these

Answer 1

Answer: (A), (B)

$Q,P$
$Q,R$

$n\left(S\right)=2\times 2\times 2=8$
$n\left(P\right)=HHT,HTH,THH,HHH=4$,
$n\left(Q\right)=TTT=1$
$n\left(R\right)=THT,HHH,HHT,THH=4$
$Q$ and $R$ and $P$ and $Q$ are nutually exclusive as they have nothing in their intersection.