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 show on the first coin", Which events are (i) mutually exclusive ? (ii) simple ? (iii) compound?

Answer 1

When three coins are tossed then S
$=\{HHH,HHT,HTH,THH,TTH,THT,HTT,TTT\}$
A: Three heads show $=\left\{HHH\right\}$
B : two heads and one tails show $=\{HHT,HTH,THH\}$
C: Three tails show $=\left\{TTT\right\}$
D: a head shows on the first coin $=\{HHH,HHT,HTH,HTT\}$
(i) Now $A\cap B=\varphi$
Thus A and B are mutually exclusive events.
$B\cap C=\varphi$
Thus B and C are mutually exclusive events.
$A\cap C=\varphi$
Thus A and C are mutually exclusive events.
$A\cap D=\left\{HHH\right\}=\ne \varphi$
Thus A and D are not mutually exclusive events.
$C\cap D=\ne$
Thus C and D are mutually exclusive events.
(ii) $A=\left\{HHH\right\},$ here n = 1
Thus A is a simple event.
$C=\left\{TTT\right\}$ Here n = 1
Thus C is a simple event.
(iii) $B=\{HHT,HTH,THH\},$ here n = 3 > 1
Thus B is a compound event.
$D=\{HHH.HHT,HTH,HTT\}$
here n = 4 > 1
Thus D is a compound event.