hurdle problem from miscellaneous cbse ncert mathematics probability

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] = _nC_r p^rq^(n-r) , r = 0,1,2,...,n

P[X=r] = ₁₀C_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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