# Expected Value

A box contains 25 balls which are numbered from $$1$$ to $$25$$. I took a ball.What is the expected number that the ball have?

Note by Kiriti Mukherjee
5 years ago

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The answer is $$13$$. [provided that all the balls have an equal chance of being selected]

The expected value of a random variable is the weighted average of all possible outcomes.

In your example the probability of a ball being selected is $$\frac{1}{25}$$. So the expected value would be:

$$1(\frac{1}{25})+2(\frac{1}{25})+3(\frac{1}{25})+4(\frac{1}{25})+\cdots + 23(\frac{1}{25})+ 24(\frac{1}{25})+25(\frac{1}{25})$$

$$=13$$.

Hope this helps!

- 5 years ago

wen all are equiprobable how can one of them(13) have more chances of appearing

- 5 years ago

If I choose a ball again with out replace the first ball .What is the expected value of the second ball?

- 5 years ago

We are not here to solve problems for you. Mursalin H. told you how to solve the first problem, and if you understand it completely, you should be able to solve this one yourself. I have also provided you with the Brilliant post about the expected value, which will help you understand the concept.

- 5 years ago

Just call me Mursalin. Mursalin H. sounds really odd! :)

- 5 years ago

You might want to read this: Expected Value | Brilliant

- 5 years ago

You probably wanted to post this link.

- 5 years ago

Thanks for pointing that out, I've updated it.

- 5 years ago