If you flip a fair coin 10 times, what is the probability of flipping exactly 8 heads?

Instruction: Calculate the probability of exactly eight heads in ten independent tosses of a fair coin. Distinguish it from at least eight heads.

Context: This question tests the candidate's understanding of binomial probability.

Updated

Official answer

With ten independent fair tosses, the head count is binomial with n=10 and p=1/2. Choose the eight positions containing heads; each resulting ten-toss sequence has probability 1/1024.

P(X=8) = C(10,8)(1/2)^8(1/2)^2 = 45/1024 ≈ 4.39%.

This is exactly eight heads. At least eight would also include nine and ten, giving (45+10+1)/1024 = 7/128, about 5.47%.

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