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,

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

A:getting three heads

B:getting at least 2 heads

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

Since

(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