# what is the probability of obtaining 8 heads in a row when flipping a fair coin? interpret this probability.

Question

what is the probability of obtaining 8 heads in a row when flipping a fair coin? interpret this probability.

Step 1

A fair coin is one which is equally likely to land on head  or on tail. So, we infer P(H) = P(T).

Since Head and Tail are the only possible outcomes, we deduce P(H) + P(T) = 1 which gives us P(H) = P(T) = 0.5

We also know that every coin flip is an independent event, so probabilty of 8 heads in a row will be given by:

P = P(H) * P(H) * P(H) * P(H) * P(H) * P(H) * P(H) * P(H)  = 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5 * 0.5  = 0.5 ^ 8 = 0.00390625

Step 2

In order to interpret this, let's consider 1 coin flip.

In 1 coin flip , the probability of getting a head is 0.5 (H, T).

In 2 coin flips, the probability of getting 2 heads in a row is 0.25 ( HH, HT, TH, TT) which is 0.5^2

In 3 coin flips, the probability of getting 3 heads in a row is 0.125 ( HHH, HTH, HHT, HTT, THH, THT, TTH, TTT) which is 0.5^3

In 4 c...

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