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  • Need clarity, kindly explain! - Statistics and Probability - JEE Main-2

Consider 5 independent Bernoulli's trials each with probability of success p . If the probability of at least one failure is greater than or equal to \frac{31}{32} , then p lies in the interval

  • Option 1)

    \left [ 0,\frac{1}{2} \right ]\;

  • Option 2)

    \; \left ( \frac{11}{12},1 \right ]\; \;

  • Option 3)

    \; \; \left ( \frac{1}{2},\frac{3}{4} \right ]\; \;

  • Option 4)

    \; \; \left ( \frac{3}{4},\frac{11}{12} \right ]\; \; \;

 

Answers (1)

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

-

 

 Probability of atleast one failure \geqslant \frac{31}{32}

 Probability of no failure \leq \frac{1}{32}

\Rightarrow Probability \:of \:all\: success=\:p^5\leqslant \frac{1}{3}

p\leqslant (\frac{1}{32})^\frac{1}{5}\leqslant \frac{1}{2}

 


Option 1)

\left [ 0,\frac{1}{2} \right ]\;

Correct

Option 2)

\; \left ( \frac{11}{12},1 \right ]\; \;

Incorrect

Option 3)

\; \; \left ( \frac{1}{2},\frac{3}{4} \right ]\; \;

Incorrect

Option 4)

\; \; \left ( \frac{3}{4},\frac{11}{12} \right ]\; \; \;

Incorrect

Posted by

Sabhrant Ambastha

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