# How to find most likely number?

Probability that an apple picked at random from a sack is bad is 0.15.

What’s the most likely number of bad apples in a sample of 30 apples?

The answer is 4

### 2 Answers

- rotchmLv 73 months agoFavorite Answer
If you have N apples to choose from, there are then on average 0.15 * N bad ones.

With N=30 this gives 4.5 bad apples.

Since you can only have integer # of apples, then you must look at the closest possibilities (because we assume that the distribution is bell shaped). So lets look at

m = 4 and m = 5.

To have exactly m bad ones, we use:

https://en.wikipedia.org/wiki/Binomial_distributio...

That is,

Prob_exactly _m_bad = 30Cm * 0.15^m * (1-0.15)^(30-m).

If m = 4 what do you get?

If m = 5 what do you get?

Which is higher (meaning, more likely).

that's your answer.

Done!

- Wayne DeguManLv 73 months ago
P(bad) = 0.15

From a batch of 30 we would have 30(0.15) => 4.5

so, 4 or 5 apples

:)>