[molsen]

A bag of marbles contains 8 red marblese, 3 green marbles, 7 black marbles, and 9 blue marbles. What is the probability of drawing 1 marble of each colour when 4 marbles are withdrawn with replacement?

Who can help me??

[galactus]

You could set this up in different ways.



or




Do you see how I arrived at those?

[molsen]

You could set this up in different ways.



or




Do you see how I arrived at those?.

i understand the 2nd way you showed me.. but i don't quite understand the first. What does the 24 denote?

[galactus]

Let's say for our forst draw we draw a red, the probability of that is 8/27.

There is one less marble in the bag, so the prob of drawing a green is 3/26

and so on.

The 24 is 4! That's because the marbles do not come out in any specific order.

The number of ways to arrange 4 different items is 4!=24 ways.

See?

[molsen]

The question states WITH replacement. The marbles are placed back into the bag after they are drawn

[galactus]

Oh, I'm sorry. DUH. That just changes things a bit.

Then it would be:

24(8/27)(3/27)(7/27)(9/27).

See? The contents of the bag reamin at 27 because the marbles are replaced. We still need to multiply by 4! Because of the order in which the marbles may come out.

There are 4! Ways to arrange 4 items.

The marbles may be drawn out in 24 different ways:

Blue, green, black, red
Red, blue, green, black
Red, black, blue, green
.
.
.
.
.

And so on.

[molsen]

Okay that makes sense. Thank you very very much!