The distribution of the number of fair coin tosses before one observed three heads in a row is 14.
We have a coin. We have to find the number of fair coin tosses before one observes three heads in a row. We need to use the Markov chain. The probability of getting a head when a coin is flipped is 1/2. Let the probability be represented by the variable "p". Let the number of heads we want in a row be "n".
p = 1/2
n = 3
Using the Markov chain, the formula for getting "n" numbers of the same event in a row with the probability "p" is given below.
A(n) = [1 - p^(n)]/[(1 - p)*p^(n)]
We need to find the value of A(3).
A(3) = [1 - (0.5)^(3)]/[(1 - 0.5)*(0.5)^(3)]
A(3) = [1 - 0.125]/[(0.5)*(0.125)]
A(3) = 0.875/0.0625
A(3) = 14
Hence, the number of fair coin tosses before one observes three heads in a row is 14.
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