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?

Asked by Abhisek | 11 months ago | 136

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)** Event A and B; event A and C; event B and C; and event 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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