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?

Answer

N/a

Explanation

It is an experiment of Bernaulli's trial where the success of this experiment is to clear a hurdle without knock down and total number of hurdles are `n=10`.
`:.p=P` (succeess) `=5/6impliesq=1-p=1/6` ltbgt Let `X` be a random variable which represents that the player is not able to clear the hurdle.
Clearly the distribution `X` is a Binomial distribution with `n=10,p=5/6` and `q=1/6`
`:.P(X=r)=.^(n)C_(r)q^(n-r).p^(r)=.^(10)C_(r)(1/6)^(r)(5/6)^(10-r)`
`P` (player will knock down fewer than 2 hurdles)
`=P(Xlt2)`
`=P(0)+P(1)=.^(10)C_(0)p^(10)q^(0)+.^(10)C_(1)p^(9)q`
`=.^(10)C_(0)(5/6)^(10)(1/6)^(0)+.^(10)C_(1)(5/6)^(9)(1/6)^(1)`
`=1xx1xx(5/6)^(10)+10xx(5/6)^(9)xx(1/6)`
`=(5/6)^(9)(5/6+10/6)`
`=15/6xx(5/6)^(9)=5/2xx(5^(9))/(6^(9))=(5^(10))/(2xx6^(9))`