In a hurdle race, a player has to cross 10 hurdles. The probability that he clear each hurdle is $$\cfrac{5}{6}$$ . What is the probability that he will knock down fewer than 2 hurdles?

.: We have $q = \cfrac{5}{6},p = 1 - \cfrac{5}{6} = \cfrac{1}{6}$ and $n = 10$

Required probability $= P(X < 2) = P(X = 0) + P(X = 1)$

${ = ^{10}}{C_0}{q^{10}}{p^0}{ + ^{10}}{C_1}{q^9}{p^1} = (1){\left( {\cfrac{5}{{10}}} \right)^{10}}(1) + (10){\left( {\cfrac{5}{6}} \right)^9}\left( {\cfrac{1}{6}} \right)$

$= {\left( {\cfrac{5}{6}} \right)^9}\left[ {\cfrac{5}{6} + \cfrac{{10}}{6}} \right] = \cfrac{5}{2}{\left( {\cfrac{5}{6}} \right)^9} = \cfrac{{{5^{10}}}}{{2 \times {6^9}}}$