Symmetry - In a bag of marbles, there are 3 red... G5 Ch7 P4

[mjschlotterbeck]

Guide 5, 5th Edition, Chapter 7, Problem 4

In a bag of marbles, there are 3 red, 2 white, and 5 blue. If Bob takes 2 marbles out of the bag, what is the probability that he will have one white and one blue marble? (Assume no placement)

I am curious if it is possible to solve this problem using a symmetry argument? The probability of getting white then blue or blue then white should be the same. Does that mean this problem is symmetric or is the fact that there are red marbles in the mix disrupt the symmetry?

I think it can be solved using symmetry like this:

2 white/ 10 total x 5 blue / 10 total = 10/90 = 1/9 chance of getting white then blue (which is same as blue then white)

There are two "winning possibilities" - 2! = 2

Equal Probability x Winning Combos = Answer
(1/9) * 2 = 2/9 chance of pulling a white and blue

Is this correct? I am still not sure if I should be correcting for the red marbles somewhere?

[jnelson0612]

Guide 5, 5th Edition, Chapter 7, Problem 4

In a bag of marbles, there are 3 red, 2 white, and 5 blue. If Bob takes 2 marbles out of the bag, what is the probability that he will have one white and one blue marble? (Assume no placement)

I am curious if it is possible to solve this problem using a symmetry argument? The probability of getting white then blue or blue then white should be the same. Does that mean this problem is symmetric or is the fact that there are red marbles in the mix disrupt the symmetry?

I think it can be solved using symmetry like this:

2 white/ 10 total x 5 blue / 10 total = 10/90 = 1/9 chance of getting white then blue (which is same as blue then white)

There are two "winning possibilities" - 2! = 2

Equal Probability x Winning Combos = Answer
(1/9) * 2 = 2/9 chance of pulling a white and blue

Is this correct? I am still not sure if I should be correcting for the red marbles somewhere?

Looks good! The reds only matter in that they contribute to the total. However, your first equation has a typo: should be "5 blue/9 total". :-) I know that's what you meant!

[mjschlotterbeck]

Jamie, thanks for the confirmation and reading through my typo! Much appreciated.

[jlucero]

Glad it helped.