In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is What is the probability that the will knock down fewer than 2 hurdles? - Wired Faculty

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

Solution

Here n = 10
Probability of clearing each hurdle = $5 over 6$
Let p be the probability of knocking each hurdle
$therefore space space space straight p space equals space 1 minus 5 over 6 space equals space 1 over 6 therefore space space space straight q space equals space 1 minus straight p space equals space 1 minus 1 over 6 space equals space 5 over 6$
P(fewer than 2 hurdles) = P(0) + P(1)
$equals space straight C presuperscript 10 subscript 0 space open parentheses 5 over 6 close parentheses to the power of 10 plus straight C presuperscript 10 subscript 1 open parentheses 5 over 6 close parentheses to the power of 9 space open parentheses 1 over 6 close parentheses space equals space open parentheses 5 over 6 close parentheses to the power of 10 space plus space 10 space cross times open parentheses 5 over 6 close parentheses to the power of 9 space cross times 1 over 6 equals space open parentheses 5 over 6 close parentheses to the power of 10 space left square bracket 1 plus 2 right square bracket space equals space 3 space open parentheses 5 over 6 close parentheses to the power of 10$

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Probability

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

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