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?

Accepted Solution

Answer:a.B and Cb.B is a subset of AStep-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 appearA:{HHTT,HTHT,THTH,TTHH,HTTH,THHT}B:Heads and tails alternateB={HTHT,THTH}C:First two tosses are headsC={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.