SOLUTION 2 the easy way Suppose that Alice first flips n coins then flips one

Solution 2 the easy way suppose that alice first

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Problem 3(p.31 #5 a, d).Let Ω be the sample space corresponding to three tosses of a coin. Givea verbal description of the following events:a)A={HHH, HHT, HTH, HTT}; b)B={HHH, HHT, HTH, THH}; c) Show thatAandBarenotindependent. d) Find a third event,C, so thatP(C) =12andP(ABC) =P(A)P(B)P(C). So the eventsA, B, Care not independent, but they have this property. 3
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Problem 4(p.31 #11).LetA, B,andCbe three events. Use the inclusion-exclusion formula fortwo events to derive the following inclusion-exclusion formula for three events:P(ABC) =P(A) +P(B) +P(C)-P(AB)-P(AC)-P(BC) +P(ABC).
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