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

Solution:

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 (no common element).

(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 i.e.,

A = {TTT}

B = {HTT, THT, TTH}

C = {HHH, HHT, HTH, THH}

This is because A ∩ B = B ∩ C = C ∩ A = Φ and A υ B υ 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 i.e.,

A = {HTT, THT, TTH}

B = {HHT, HTH, THH}

This is because A ∩ B = Φ but A υ 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 i.e.,

A = {HHH}

B = {HTT, THT, TTH}

C = {HHT, HTH, THH}

This is because A ∩ B = B ∩ C = C ∩ A = Φ but A υ B υ C ≠ S

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NCERT Solutions Class 11 Maths Chapter 16 Exercise 16.2 Question 5

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

Summary:

(i) A: getting no heads and B: getting no tails. (ii) A: getting no heads and B: getting exactly one head C: getting at least two heads (iii) A: getting three heads and B: getting at least 2 heads (iv) A: getting exactly one head and B: getting exactly one tail (v) A: getting exactly three heads, B: getting one head and two tails and C: getting one tail and two heads