Question

Find the probability that a person flipping a coin gets (a) the third tail on the eleventh flip, and (b) the first tail on the tenth flip

Answer 1

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

a) P(heads), p = 0.5

P(tails), q = 0.5

P(third tail on the eleventh flip) = P(10 heads and 2 tails on 12 flips) x P(tail on 13th flip)

= 12C2x0.5¹² x 0.5

= 0.0081

b) P(first tail on 10th flip) = P(9 heads on first 9 flips) x P(tail on 10th flip)

= 0.5⁹ x 0.5

= 0.00098