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3. A coin is tossed four times and the resulting sequence of heads and/or tails is recorded. Define the events A, B, and C as follows: A: exactly two heads appear B: heads and tails alternate C: first two tosses are heads (a) Which events, if any, are mutually exclusive? (b) Which events, if any, are subsets of other sets?

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Answer:

a.B and C

b.B is a subset of A

Step-by-step explanation:

We are given that a coin is tossed four times

Sample space={HHHH,HTTT,HHTT,HTHT,THTH,TTTH,TTHH,HTTH,THHT,HHHT,THHH,TTTT,HHTH,TTHT,THTT,HTHH}

A:Exactly two heads appear

A:{HHTT,HTHT,THTH,TTHH,HTTH,THHT}

B:Heads and tails alternate

B={HTHT,THTH}

C:First two tosses are heads

C={HHTT,HHTH,HHHH,HHHT}

a.We have to find mutually exclusive events

Mutually exclusive events: It is that events in which intersection of events is empty.

Event B and C are disjoint because [tex]A\cap B=\phi[/tex]

Hence, B and C are mutually exclusive.

b.We have to find that sets which are subset of other.

We can see that B is subset of A because all elements of B  contain in set A.

Therefore , event B is  a subset of event A.

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