Define events ac as subsets of the coin toss sample space Oh

Define events (a)-(c) as subsets of the coin toss sample space Ohm 3 = {TTT,TTH, THT, THH, HTT, HTH, HHT, HHH}. The second toss results in a head. A tail conies before a head. No heads. Assuming that P (Head) = 1/3 find the probabilities of these events.

Solution

a)

{THT, THH, HHT, HHH}

Here, P(H) = 1/3, P(T) = 2/3.

Thus,

P(a) = (2/3)(1/3)(2/3) + (2/3)(1/3)(1/3) + (1/3)(1/3)(2/3) + (1/3)(1/3)(1/3) = 1/3 [ANSWER]

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b)

{TTH, THT, THH}

P(b) = (2/3)(2/3)(1/3) + (2/3)(1/3)(2/3) + (2/3)(1/3)(1/3) = 10/27 [ANSWER]

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c)

{TTT}

P(c) = (2/3)(2/3)(2/3) = 8/27 [ANSWER]

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