1. Tardigrade
  2. Question
  3. Mathematics
  4. In a binomial distribution, the sum of its mean and variance is 1.8. Find the probability of two successes, if the event was conducted 5 times.

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. In a binomial distribution, the sum of its mean and variance is $1.8$. Find the probability of two successes, if the event was conducted $5$ times.

Probability - Part 2

Solution:

Here $np + npq = 1.8$ and $n = 5$
$\Rightarrow 5p\left(1 + q\right) = 1.8$
$\Rightarrow \left(1 -q\right)\left(1 + q\right) = 0.36$
$\Rightarrow 1 - q^{2}= 0.36$
$\Rightarrow q^{2} = 0.64$
$\Rightarrow q = 0.8$ (Taking + ve value only)
$\therefore n = 5$, $p = 0.2$, $g = 0.8$
$\therefore $ Probability of $2$ successes $= P\left(2\right) =\,{}^{5}C_{2}p^{2}q^{3}$
$= 10\left(0.2\right)^{2}\, \left(0.8\right)^{3} = 0.2048$