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”. Which events are
(i) mutually exclusive?   (ii) simple?   (iii) compound?

Solution:

When three coins are tossed, the sample space is given by

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

According to the definitions of the events A, B, and C given in the problem,

A = {HHH}

B = {HHT, HTH, THH}

C = {TTT}

D = {HHH , HHT, HTH, HTT}

We can 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

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NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.2 Question 4

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”. Which events are (i) mutually exclusive? (ii) simple? (iii) compound?

Summary:

(i) Events A and B; events A and C; events B and C; and events C and D are all mutually exclusive (ii) A and C are simple events (iii) B and D are compound events