A fair coin is tossed three times The sample space is HHH HH

A fair coin is tossed three times. The sample space is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. Event A: The first toss is a head. Event B: at least one result is a tail. Event C: at least one result is head.

a. List the outcomes of event ‘A and B’ A and B = { }

b. Find P(B or C)

Solution

a)

A and B means:

The first toss is a head AND at least one result is a tail.

Thus,

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

Getting the intersection,

A and B = {HHT, HTH, HTT} [ANSWER]

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b)

Here,

B or C means: At least one result is a tail OR at least one result is head

which is a sure event! It is always the case that there is a head or a tail, becasue those are the only results possible.

Thus,

P(B or C) = 1 [ANSWER, SURE EVENT]