# 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? - Mathematics

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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#### APPEARS IN

NCERT Class 12 Maths
Chapter 13 Probability
Q 6 | Page 583