Question

Find the probability that a person flipping a coin gets (a) the second head on the ninth flip, and (b) the first head on the third flip. . (a) The probability that a person flipping a coin gets the second head on the ninth flip is (Round to four decimal places as needed.)

Answer 1

P(Head), p = 0.5

q = 1 - p = 0.5

Binomial distribution: P(X) = nCx p^x q^n-x

a) P(the second head on ninth flip) = P(1 Head in first 8 flips and head on 9th flip)

= (8C1 x 0.5⁷ x 0.5) x 0.5

= 0.0156

b) P(first head on third flip) = P(Tails on first 2 flips) x P(Heads on 3rd flip)

= 0.5² x 0.5

= 0.125