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?

Let
X be the number of hurdles the player knocks down out of 10 hurdles

Assume
X follows binomial distribution with

n=10

p
= 1-(5/6) [because we defined X in terms of the
hurdles knocked down ]

p=(1
/6)

q
= 1 -p

q
=(5/6)

P[X=r]
=

_{n}C_{r }p^{r}q^{(n-r) }, r = 0,1,2,...,n
P[X=r]
=

_{10}C_{r }(1/6)^{r}(5/6)^{(10 - r) }, r = 0,1,2,...,10
P[the
player will knock down fewer than two hurdles] = P[ X < 2 ]

P[
X < 2 ] = P[X=0] + P[X=1]

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