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The random variable x represents the number of numbers on the toss of five coins

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 The random variable x represents the number of numbers on the toss of five coins. Determine the value:

a. P(x < 1)

b. P(x < 2)

c. P(x < 3)

d. P(x < 4)

Answer:

S = {AAAAA, AAAAG, AAAGA, AAGAA, AGAAA, GAAAA, AAAGG, AAGAG, AAGGA, AGAAG, AGAGA, AGGAA, GAAAG, GAAGA, GAGAA, GGAAA, AAGGG, AGAGG, AGGAG, AGGGA, GAAGG, GAGAG, GAGGA, GGAGA, GGAAG, GGGAA, AGGGG, GAGGG, GGAGG, GGGAG, GGGGA, GGGGG}

X = {0,1,2,3,4,5}

a. P(x < 1) = f(0) + f(1) = 1/32 + 5/32 = 6/32 = 3/16

b. P(x < 2) = P(x < 1) + f(2) = 6/32 + 10/32 = 16/32 = 1/2

c. P(x < 3) = P(x < 2) + f(3) = 16/32 + 10/32 = 26/32 = 13/16

d. d. P(x < 4) = P(x < 3) + f(4) = 26/32 + 5/32 = 31/32

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