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In a binomial distribution `B(n , p=1/4)` , if the probability of at least one success is greater than or equal to `9/(10)` , then n is greater than (

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In a binomial distribution B(n,p= 1 4 ) , if the probability of at least one success is greater than or equal to 9 10 , then n is greater than (1) 1 (log) 4 10 -(log) 3 10 (2) 1 (log) 4 10 +(log) 3 10 (3) 9 (log) 4 10 -(log) 3 10 (4) 4 (log) 4 10 -(log) 3 10 A. 1 log104-log103 B. 1 log104+log103 C. 9 log104-log103 D. 4 log104-log103 Select the correct answer from above options

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Correct Answer - A Let X be the binomial variate. Then, P(X≥1)≥ 9 10 ⇒1-P(X=0)> 9 10 ⇒P(X=0)< 1 10 ⇒.Nc0( 1 4 )0( 3 4 )n< 1 10 ⇒nlog10( 3 4 )1⇒n> 1 log104-log1010

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