Three coins are tossed. Describe (i) Two events which are mutually ex

1.	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.
Answer» Let (i) A: ‘atleast two heads appear’ B: ‘atleast two tails appear’ Here, A = {HHT, HTH, THH, HHH} B = {TTH, THT, HTT, TTT} ∴ A ∩ B = ϕ , ⇒ A, B mutually exclusive. (Note: Give any suitable example (events) associated with experiment) (ii) Let A : ‘No tail appears’ B: ‘Exactly one tail appears’ C: ‘Atleast two tails appear’ Here A = {HHH] B = {THH, HTH, HHT} C = {TTH, THT, HTT, TTT} Clearly, A ∪ B ∪ C = sample space = S and A ∩ B = ϕ , B ∩ C = ϕ, A ∩ C ∴ A, B, C are mutually exclusive and mutually exclusive and exhaustive events. (iii) Let A: ‘almost two tails appear’ B: ‘exactly two tails appear’ Here, A = {HHH, THH, HTH, HHT, HTT, THT, TTH} B = {HTT,THT,TTH} Clearly, A ∩ B ≠ ϕ ∴ A and B are not mutually exclusive (iv) ‘Getting exactly one head’ and ‘Getting exactly two heads’. (v) ‘Getting exactly one tail’, ‘Getting exactly two tails’ and ‘Getting exactly three tails’.

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.

Answer»

Let

(i)

A: ‘atleast two heads appear’

B: ‘atleast two tails appear’

Here, A = {HHT, HTH, THH, HHH}

B = {TTH, THT, HTT, TTT}

∴ A ∩ B = ϕ , ⇒ A, B mutually exclusive.

(Note: Give any suitable example (events) associated with experiment)

(ii) Let A : ‘No tail appears’

B: ‘Exactly one tail appears’

C: ‘Atleast two tails appear’

Here A = {HHH]

B = {THH, HTH, HHT}

C = {TTH, THT, HTT, TTT}

Clearly, A ∪ B ∪ C = sample space = S and A ∩ B = ϕ , B ∩ C = ϕ, A ∩ C

∴ A, B, C are mutually exclusive and mutually exclusive and exhaustive events.

(iii) Let

A: ‘almost two tails appear’

B: ‘exactly two tails appear’

Here,

A = {HHH, THH, HTH, HHT, HTT, THT, TTH}

B = {HTT,THT,TTH}

Clearly, A ∩ B ≠ ϕ

∴ A and B are not mutually exclusive

(iv) ‘Getting exactly one head’ and ‘Getting exactly two heads’.

(v) ‘Getting exactly one tail’, ‘Getting exactly two tails’ and ‘Getting exactly three tails’.