JEE Main 2023 — Probability Question with Solution

There rotten apples are mixed accidently with seven good apples,

And four apples are drawn one by one without replacement.

Now the random variable X denote the number of rotten apples.

And $\mu$ and ${\sigma }^2$ represent mean and variance of X, respectively, 

So, now plotting the table of given data we get,

Now mean is given by, $\sum xP\left(x\right)=\frac{6}{2}=\mu$

And variance is given by ${\sigma }^2=\sum x^{2}P\left(x\right)-{\mu }^2$

So, by putting the value from above table we get,  ${\sigma }^2+{\mu }^2=0+\frac{1}{2}+\frac{12}{10}+\frac{9}{30}=2$

Hence, $10\left({\sigma }^2+{\mu }^2\right)=20$