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]
= nCr prq(n-r) , r =
0,1,2,...,n
P[X=r]
= 10Cr (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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