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Question

In n independent trials (finite) of a random experiment, let X be the number of times an event A occurs. If the probability of success of one trial say p and we get the probability of failure of event A i.e. P(¯A)=1p=q. The probability of r success in n trials is denoted byP(X=r) such that P(X=r)=nCrprqnr, known as binomial distribution of random variable X. We also have the following result-
(i) Probability of getting at least k successes is
P(XK)=nr=k nCrprqnr
(ii) Probability of getting at the most k successes is
P(XK)=nr=0 nCrprqnr
(iii) nr=0=nCrprqnr=(p+q)n=1

On the basis of above information answer the following question.

In a hurdle race, a player has to cross 10 hurdles.The probability that he will cross each hurdle is 56, then the probability that he will knock down fewer than two hurdle is

A
7(56)10
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B
5(56)10
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C
3(56)10
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D
35(56)10
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Solution

The correct option is B 3(56)10
Here ,n=10,p= knocking down the hurdle =16

and q= Clearing the hurdle =56

Using P(X=r)=10Cr(16)r(56)10r

Required probability

=P(X=r<2)=P(0)+P(1)=(56)10+(10)16(56)9=(56+106)(56)9=3(56)10

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