Three coins are tossed once. Describe the following events associated with this random experiment:
A = Getting three heads, B = Getting two heads and one tail, C = Getting three tails, D = Getting a head on the first coin.
(i) Which pairs of events are mutually exclusive?
(ii) Which events are elementary events?
(iii) Which events are compound events?
Given: There are three coins tossed once.
To Find: Describe the events according to the subparts?
Explanation: when three coins are tossed, then the sample spaces are:
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
According to the question,
A = {HHH}
B = {HHT, HTH, THH}
C = {TTT}
D = {HHH, HHT, HTH, HTT}
Now,
Since, If the intersection of two sets are null or empty it means both the sets are Mutually Exclusive.
(i) Events A and B, Events A and C, Events B and C and events C and D are mutually exclusive.
(ii) Here, We know, If an event has only one sample point of a sample space, then it is called elementary events.
So, A and C are elementary events.
(iii) If There is an event that has more than one sample point of a sample space, it is called a compound event,
Since,
So, B and D are compound events.