Answer 1

Let p and q respectively be the probabilities that the player will clear and knock down the hurdle.

`:. p = 5/6`

`q = 1 - p = 1 - 5/6 = 1/6`

Let X be the random variable that represents the number of times the player will knock down the hurdle.

Therefore, by binomial distribution, we obtain

P (X = x) = `""^nC_x p^(n-x) q^x`

P (player knocking down less than 2 hurdles) = P (X < 2)

= P (X = 0) + P (X = 1)