Question

A bag contains some number of marbles. It is known that 20 of them are red. When 15 marbles are drawn, without replacement, we get 6 red. Assuming E(X)=6 red, what is the total number of marbles in the bag?

Answer 1

Answer:

The total number of marbles in the bag is 50.

Step-by-step explanation:

Here, we have n trials, without replacement. So the hypergeometric distribution is used.

The mean of the hypergeometric distribution is:

$E(X) = \frac{n*k}{N}$

In which n is the number of items in the sample, k is the number of items in the population that are classified a success and N is the size of the population.

15 marbles are drawn:

This means that $n = 15$

A bag contains some number of marbles. It is known that 20 of them are red.

This means that $k = 20$, since a success is drawing a red marble.

Assuming E(X)=6 red, what is the total number of marbles in the bag?

We have to find N when $E(X) = 6$

So

$E(X) = \frac{n*k}{N}$

$6 = \frac{15*20}{N}$

$6N = 300$

$N = \frac{300}{6}$

$N = 50$

The total number of marbles in the bag is 50.