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  4. A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, the (( textmean textof X/ textstandard textdeviation textof X )) is equal to :

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Q. A bag contains $30$ white balls and $10$ red balls. $16$ balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, the $\left(\frac{\text{mean} \; \text{of} \; X}{\text{standard} \; \text{deviation} \; \text{of} \; X }\right)$ is equal to :

JEE MainJEE Main 2019Probability - Part 2

Solution:

p (probability of getting white ball) = $\frac{30}{40}$
$q = \frac{1}{4}$ and n = 16
mean =np = $ 16 . \frac{3}{4} = 12$
and standard diviation
$ = \sqrt{npq} = \sqrt{ 16 . \frac{ 3}{4} . \frac{1}{4}} = \sqrt{3}$