Question

A small glass jar is filled with colorful marbles. Six are blue, eight are yellow, five are green, and eleven are red. Marbles are chosen randomly from the jar one at a time without replacement. What is the probability of choosing two red marbles?

Answer 1

So we have a jar full of marbles of different colors. The probability of choosing a marble of a certain color is given by:

`P=\frac{\text{Number of marbles of that color at that time}}{\text{Total number of marbles at that time}}`

The probability of choosing two red marbles will be given by the product of two probabilities: that of choosing a red marble in the first try and that of choosing a red marble in the second try.

In order to find both we first need to find the total number of marbles that were initially. We have 6 blue marbles, 8 yellow ones, 5 green ones and 11 red ones. Then the total number of marbles at the beginning is:

`6+8+5+11=30`

Then considering there are 11 red marbles the probability of choosing a red one in the first try is:

`(11)/(30)`

Since we are taking marbles without replacement after taking the first red marble from the jar we have 10 red marbles out of 29 total marbles. Then the probability of choosing a red marble in the second try after choosing another in the first try is:

`(10)/(29)`

Then the probability of choosing two red marbles is:

`(11)/(30)\cdot(10)/(29)=(11)/(87)\cong0.126`

Then the answer is 11/87 or as a decimal number: 0.126.