In a binomial distribution, mean is 18 and variance is 12 then p = ….

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In a binomial distribution, mean is 18 and variance is 12 then p = ….

MathematicsProbabilityMHT CETMHT CET 2019 (Shift 2)

Options:

A $\frac{2}{3}$
B $\frac{1}{3}$
C $\frac{3}{4}$
D $\frac{1}{2}$

Solution:

2262 Upvotes Verified Answer

The correct answer is:

\frac{1}{3}

We know that, mean =

n p = 18

and variance

= n = p q = 12

Now,

\frac{2 p q}{n p} = \frac{12}{18} \Rightarrow q = \frac{2}{3}

∴ p = - 1 q = 1 - \frac{2}{3} = \frac{1}{3}

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