Question

Three coins are tossed once. Let $A$ denote the event "three heads show", $B$ denote the event "two heads and one tail show", $C$ denote the event "three tails show" and $D$ denote the event "a head shows on the first coin". Then, match the terms of Column I with the terms of Column II and choose the correct option from the codes given below.

Column I		Column II
A	Mutually exclusive events	1	$A$ and $B, A$ and $C, B$ and $C, C$ and $D, A, B$ and $C$
B	Simple events	2	$B, D$
C	Compound events	3	$A$ and $C$

• A. A - (2), B - (3), C - (1)
• B. A - (3), B - (2), C - (1)
• C. A - (1), B - (2), C - (3)
• D. A - (1), B - (3), C - (2)

Answer 1

Answer: (D)

When three coins are tossed, then there are $2^3=8$ possible outcomes.
i.e., $S=\{H H H, H H T, H T H, H T T, T H H, T H T, T T H, T T T\}$
$A=$ Three heads shows $=\{H H H\}$
$B=$ Two heads and one tail show
$=\{H H T, H T H, T H H\}$
$C=$ Three tails show $=\{T T T\}$
$D=$ A head shows on the first toss
$=\{H H H, H H T, H T H, H T T\}$
A. Here,
$A \cap B=\phi$
$A \cap C=\phi $
$B \cap C=\phi $
$C \cap D=\phi $
$A \cap B \cap C=\phi$
Here, $A$ and $B, A$ and $C, B$ and $C, C$ and $D$ and $A, B$ and $C$ are mutually exclusive.
B. Since, events A, C have only one sample point.
Here, $A$ and $C$ are simple events.
C. Since, events $B, D$ have two or more sample points. Hence, $B$ and $D$ are compound events.