Three coins are tossed. Describe

**(i)** Two events which are mutually exclusive.

**(ii)** Three events which are mutually exclusive and exhaustive.

**(iii)** Two events, which are not mutually exclusive.

**(iv) **Two events which are mutually exclusive but not exhaustive.

**(v) **Three events which are mutually exclusive but not exhaustive.

Asked by Abhisek | 1 year ago | 142

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

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

**(i) **Two events that are mutually exclusive can be

A: getting no heads and

B: getting no tails This is because sets

A = {TTT} and B = {HHH} are disjoint.

**(ii) **Three events that are mutually exclusive and exhaustive can be

A: getting no heads

B: getting exactly one head

C: getting at least two heads

A = {TTT}

B = {HTT, THT, TTH}

C = {HHH, HHT, HTH, THH}

This is because A ∩ B = B ∩ C =C ∩ A = φ and A U B U C = S

**(iii)** Two events that are not mutually exclusive can be A: getting three heads B: getting at least 2 heads i.e.,

A = {HHH}

B = {HHH, HHT, HTH, THH}

This is because A ∩ B = (HHH) ≠ φ

**(iv)** Two events which are mutually exclusive but not exhaustive can be

A: getting exactly one head

B: getting exactly one tail

A = {HTT, THT, TTH}

B = {HHT, HTH, THH}

This is because A ∩ B = φ, but A U B ≠ S

**(v) **Three events that are mutually exclusive but not exhaustive can be

A: getting exactly three heads

B: getting one head and two tails

C: getting one tail and two heads

A = {HHH}

B = {HTT, THT, THH}

C = {HHT, HTH, THH}

This is because A ∩ B = B ∩ C = C ∩ A= φ, but A U B U C ≠ S

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