# Picking Marbles from a bag--Probability

• Feb 24th 2011, 05:11 PM
led23
Picking Marbles from a bag--Probability
Could anyone help me out?

There are 100 marbles in a bag, 50 blue, 40 red, and 10 purple. You draw three times returning a marble to the bag each time you draw (this makes one game). What is the probability of getting 1 purple, 1blue, and 1 red? Purple, then blue, then purple? Red, then blue, then red?

I found out that there are 27 total possibilities, so would it just be # of times that it comes up/27 or would the probability of picking each marble play into this also?
• Feb 24th 2011, 05:25 PM
Quacky
P(Blue)=0.5, P(Red)=0.4, P(Purple)=0.1

This is unconditional probability as the events do not affect each other.

P(blue, red, purple once) =(0.5)(0.4)(0.1)=0.02
That is to say:

Blue, Red, Purple = 0.02.
Blue, Purple, Red = 0.02
Red, Blue, Purple = 0.02
Red, Purple, Blue = 0.02
Purple, Blue, Red = 0.02
Purple, Red, Blue = 0.02

So what is the probability of you receiving a purple, blue and red in any order?
• Feb 24th 2011, 05:32 PM
led23
Oh, so it would be a 12% chance of getting purple, blue and red in any order?

What about the other 2 then?
• Feb 24th 2011, 05:39 PM
Quacky

As I said above, P(purple) = 0.1 and P(blue) = 0.5

P(Purple, blue, purple) = (0.1)(0.5)(0.1) = 0.005
So just a 0.5% chance. Note that order is important here, so you do not write out the possible combinations.

Have an attempt at the final part yourself now.
• Feb 24th 2011, 05:46 PM
led23
Then the last one would have an 8/100 chance.

Thank you so much!
• Feb 24th 2011, 05:51 PM
Quacky
Quote:

Originally Posted by led23
Then the last one would have an 8/100 chance.

Yup.