Three coins are tossed once. Describe the following events associated

1.	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?
Answer» 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, A∩B = ϕ,A∩C = ϕ,A∩D = {HHH} B∩C = ϕ,B∩D = {HHT,HTH},C∩D = ϕ 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, B∩D = {HHT,HTH} So, B and D are compound events.

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?

Answer»

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, A∩B = ϕ,A∩C = ϕ,A∩D = {HHH}

B∩C = ϕ,B∩D = {HHT,HTH},C∩D = ϕ

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,