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?

Explanation

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

`∴p=65​`

and `p+q=1`

`⇒q=1−p=1−65​=61​`

Let X represents the number of times the player will knock down the hurdle.

Thus, by binomial distribution, we obtain

`P(X=x)=((n-x)!)/((n!)(x!))​​p^(n−x)q^x`


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