If a fair coin is tossed 8 times, then the probability of getting at most 2 heads is...

Step-by-step solution

Let X be the number of heads obtained in 8 tosses of a fair coin. The probability of getting a head is p = 1 2 and a tail is q = 1 2 . The probability of getting exactly r heads is given by P(X = r) = ⁸C_ r ( 1 2 )^r ( 1 2 )^ 8-r = ⁸C_ r 256 . The probability of getting at most 2 heads is P(X 2) = P(X = 0) + P(X = 1) + P(X = 2) . P(X 2) = ⁸C₀ 256 + ⁸C₁ 256 + ⁸C₂ 256 P(X 2) = 1 + 8 + 28 256 = 37 256 Answer: 37 256