1.

Three coins are tossed. Describe (i) two events A and B which are mutually exclusive. (ii) three events A, B and C which are mutually exclusive and exhaustive. (iii) two events A and B which are not mutually exclusive. (iv) two events A and B which are mutually exclusive but not exhaustive.

Answer»

When three coins are tossed, then the sample space is 

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

Now, The subparts are: 

(i) The two events which are mutually exclusive are when, 

A: getting no tails 

B: getting no heads 

Then, A = {HHH} and B = {TTT} 

SO, The intersection of this set will be null. 

Or, The sets are disjoint. 

(ii) Three events which are mutually exclusive and exhaustive are: 

A: getting no heads 

B: getting exactly one head 

C:getting at least two head 

So, A = {TTT} B = {TTH, THT, HTT} and C = {HHH, HHT, HTH, THH} 

Since, A∪B = B∩C = C∩A = Փ and A∪B∪C = S

(iii) The two events that are not mutually exclusive : 

A:getting three heads 

B:getting at least 2 heads 

So, A = {HHH} B = {HHH, HHT, HTH, THH} 

Since A∩B = {HHH} ≠ Փ

(iv) The two events which are mutually exclusive but not exhaustive are: 

A:getting exactly one head

B: getting exactly one tail 

So, A = {HTT, THT, TTH} and B = {HHT, HTH, THH} 

It is because A∩B = Փ but A∩B ≠ s


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