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Question
In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is 5/6 . What is the probability that he will knock down fewer than 2 hurdles?
Solution
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)
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