Probability of selecting exactly 2 red marbles out of 3 draws

Question

A bag contains 5 red marbles 9 white marbles and 5 blue marbles you draw 3 marbles out at random without replacement what is the probability of selecting exactly 2 red marbles

Answer 1

Let us first pick our variables to make this problem simpler:

R - red marble

W - white marble

B - blue marble

Using the letters we can make the bag of marbles look like this:

RRRRR

WWWWW

WWWW

BBBBB

There are a total of 19 marbles in the bag. Picking a marble out of the bag is considered an independent event. When we have independent events we multiply the probabilities together.

First we consider the probability of picking two red marbles out of the bag.

P(R then R)= (5/19)(4/18)= .0585

Then we have to consider the number of ways the event of drawing 2 red marbles out of 3 tries is:

RRW, RWR, WRR, RRB, RBR, BRR

There are six different ways we can choose two red marbles in 3 tries. Then we multiply the probability we got from before by 6:

.0585(6)= .3509