Question

There is a bag filled with 3 blue, 4 red and 5 green marbles.

A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 different colours?​

Answer 1

Using the hypergeometric distribution, it is found that there is a 0.4286 = 42.86% probability of getting 2 of the same colour.

The marbles are chosen without replacement, hence the hypergeometric distribution is used to solve this question.

What is the hypergeometric distribution formula?

The parameters are:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this problem:

There is a total of 3 + 4 = 7 marbles, hence N = 7.

Of those, 3 are blue, hence k = 3.

2 marbles will be taken, hence n = 2.

Explanation: