Question

If a fair coin is flipped 8 times, what is the probability that you obtain all 8 heads?

Answer 1

If the coin is flipped m times and if probability of getting exactly n heads = mCn x (0.5^n) x (0.5^m-n)

Here, probability of getting at least 3 heads is asked.

= 1 - ( probability of getting 0, 1 or 2 heads)

= 1- (probability of getting 0 head + probability of getting 1 head + probability of getting 2 head)

= 1 - { (8C0 x 0.5^0 x 0.5^8) + ( 8C1 x 0.5^1 x 0.5^7) + ( 8C2 x 0.5^2 x 0.5^6) }

= 1- {(1 x 1 x 0.5^8) + (8 x 0.5 x 0.5^7) + (28 x 0.5^2 x 0.5^6)}

= 1 - (0.00390625 + 0.03125 + 0.109375)

= 1 - (0.14453125)

= 0.85546875

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Answer 2

The answer is (1/2)^8=1/256