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coin is flipped four times. For each of the events described below, express the event as a set in roster notation. Each outcome is written as a string of length 4 from {H, T}, such as HHTH. Assuming the coin is a fair coin, give the probability of each event.
(a) The first and last flips come up heads.
(b) There are at least two consecutive flips that come up heads.
(c) The first flip comes up tails and there are at least two consecutive flips that come up heads.

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Answer:

(a) 25%

(b) 50%

(c) 18.75%

Step-by-step explanation:

Since there are two possible outcomes for each coin the number of total possible permutations is given by:

[tex]N=2*2*2*2=16[/tex]

(a) The first and last flips come up heads.

4 possible outcomes meet this requirement:

{HHHH}, {HHTH}, {HTHH},{HTTH}

P=4/16 = 25%

(b) There are at least two consecutive flips that come up heads.

8 possible outcomes meet this requirement:

{HHHH}, {HHHT},{HHTH} {HTHH},{THHH},{TTHH},{HHTT}, {THHT}

P=8/16 = 50%

(c) The first flip comes up tails and there are at least two consecutive flips that come up heads.

3 possible outcomes meet this requirement:

{THHH},{TTHH}, {THHT}

P=3/16 = 18.75%

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