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Home » In a hurdles race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is . What is the probability that he will knock down fewer than 2 hurdles?
In a hurdles 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?
Binomial Distribution | CBSE | Class 12 | Exercise 32A | Maths | RS Aggarwal
In a hurdles 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?

The probability that the hurdle will be cleared is 5 / 6
Using Bernoulli’s Trial we have,
\begin{array}{l} P(\text { Success }=x)={ }^{n} C_{x} \cdot p^{x} \cdot q^{(n-x)} \\ x=0,1,2, \ldots \ldots . n \text { and } q=(1-p), n=10 \\ p=5 / 6 q=1 / 6 \end{array}
Probability that he will knock down fewer than 2 hurdles is =
\begin{array}{l} P(0)+P(1) \\ \Rightarrow{ }^{10} C_{0}\left(\frac{1}{6}\right)^{0}\left(\frac{5}{6}\right)^{10}+{ }^{10} C_{1}\left(\frac{1}{6}\right)^{1}\left(\frac{5}{6}\right)^{9} \\ \Rightarrow \frac{5^{10}}{2 \times 6^{9}} \end{array}

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