In a binomial distribution B\left ( n,p= \frac{1}{4} \right ), if the probability of at least one success is greater than or equal to \frac{9}{10},then n is greater than

  • Option 1)

    \frac{1}{\log_{10}4+\log_{10}3}

  • Option 2)

    \frac{9}{\log_{10}4-\log_{10}3}

  • Option 3)

    \frac{4}{\log_{10}4-\log_{10}3}

  • Option 4)

    \frac{1}{\log_{10}4-\log_{10}3}

 

Answers (1)
V Vakul

As we learnt in

Binomial Distribution -

Let E be an event and p+q = 1 then

X :          0                         1                            2         ..................     n

P(x):      qn                   {^n}c_1\cdot p^{1}q^{n-1}           {^n}c_2\cdot p^{2}q^{n-2}            pn

-

 

 1-\left ( \frac{3}{4} \right )^{n}\geq \frac{9}{10}

\left(\frac{3}{4} \right )^{n}\leq 1- \frac{9}{10}=\frac{1}{10}

\left(\frac{4}{3} \right )^{n}\geq 10

\Rightarrow    n [log 4 - log 3]\geq log 10

Thus 

n\geq\frac{1}{log4-log3}


Option 1)

\frac{1}{\log_{10}4+\log_{10}3}

this is incorrect option

Option 2)

\frac{9}{\log_{10}4-\log_{10}3}

this is correct option

Option 3)

\frac{4}{\log_{10}4-\log_{10}3}

this is incorrect option

Option 4)

\frac{1}{\log_{10}4-\log_{10}3}

this is incorrect option

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