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

$fraction numerator 1 over denominator log space subscript 10 superscript 4 minus log subscript 10 superscript 3 end fraction$
$fraction numerator 1 over denominator log space subscript 10 superscript 4 space plus space log space subscript 10 superscript 3 end fraction$
$fraction numerator 9 over denominator log subscript 10 superscript 4 minus space log subscript 10 superscript 3 end fraction$
$fraction numerator 4 over denominator log subscript 10 superscript 4 minus space log subscript 10 superscript 3 end fraction$

Solution

fraction numerator 1 over denominator log space subscript 10 superscript 4 minus log subscript 10 superscript 3 end fraction

1 minus straight q to the power of straight n space greater or equal than 9 over 10 rightwards double arrow space open parentheses 3 over 4 close parentheses squared space less or equal than space 1 over 10 space rightwards double arrow space straight n space greater or equal than space minus space log subscript 3 over 4 end subscript space 10 rightwards double arrow space straight n space greater or equal than space fraction numerator 1 over denominator log subscript 10 superscript 4 minus log subscript 10 superscript 3 end fraction

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