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 $D$ denotes the event a head shows on the first coin”. Which events are (I) mutually exclusive? (ii) simple? (iii) Compound?

Answer 1

When three coins are tossed, the sample space is given by
$S = \\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\\}$
Accordingly,
$A = \\{HHH\\}$

$B = \\{HHT, HTH, THH\\}$
$C = \\{TTT\\}$
$D = \\{HHH, HHT, HTH, HTT\\}$
We now observe that,
$A ∩ B =Φ, A ∩ C =Φ, A ∩ D = \\{HHH\\} ≠ Φ$
$B ∩ C =Φ, B ∩ D = \\{HHT, HTH\\} ≠ Φ$
$C ∩ D = Φ$
(i) Events $A$ and $B;$ Events A and $C;$ Events $B$ and $C;$ and Events $C$ and $D$ are all mutually exclusive.
(ii) If an event has only one sample point of a sample space, it is called a simple event. Thus, $A$ and $C$ are simple events.
(iii) If an event has more than one sample point of a sample space, it is called a compound event. Thus, $B$ and $D$ are compound events.