math forumla question

Anon

How can i show this puzzle in a mathematical equation, or php?

I have 4 balls in a bag:

2 purple
1 white
1 yellow

I take out 2 balls and 1 of them is purple.

What are the chances that the other ball I took out is purple?

please help me .. and even if you don't know how to put it in an equeation.. let me know what you think the answer is.

Sorry if it's a bit off the topic, .. but programmers are the only people i think can help me on this one =) thanks.

[deleted]

Sounds like a school-assigment long over due?

Anon

no, .. actually a debate with a collegue over the correct answer.

He seems to think the answer is 1 in 5 because of the possibilities of drawing 2 balls.. this was a question in a book that is supposed to be very credible.

i'm trying to disprove their logic .. every way i do it, it seems to be 1 in 3.

yes there are 2 purple balls, but we must look at them as if they were 2 different colors because we already know where 1 purple ball is.

anyhow, thanks for at least looking.

Anon

2 purple
1 white
1 yellow

                I take out 2 balls and 1 of them is purple. 

                What are the chances that the other ball I took out is purple?

You have a total of 4 balls in the bag at the beginning. You removed one purple, bringing the total down to 3 (one purple, white, & yellow). Since there are three balls left, and one is purple, the answer must be 1/3.

The answer of 1 out of 5 is illogical.... you only have a total of four balls to begin with, how would you get a denominator of 5, as the denominator is always the total?

Anon

I agree; it should be 1/3

Diego

Anon

ok.. after showing this post .. i was corrected. here is the exact wording of the puzzle. is it still the same answer?

"Four colored balls are placed in a bag. One is white, one is yellow, and two are purple. I draw two balls from the bag and place one of them, which is purple, on a table. What are the chances the second ball I still have in my hand is the other purple ball?"

[deleted]

Hmm yes it is 1/3, not 1/5

I think your collegue is mistakenly thinking about "what are the changes of picking both purple balls"

But the fact that the first purple ball was picked is a given, that fact has a 100% probability, thus the only chance remaining is the chance of picking the 'other' purple ball from the remaining three balls, which is 1/3.

Here's another riddle for you though.
Assume you're playing the infamous ball-and-cup game, where you have three cups with a ball under one cup.

Now, after the dealer shuffles the cups, you get to choose one cup, but you can't lift it up yet. Now the dealer will lift one of the remaining cups to show wether that one has the ball under it or not. Now he gives you a chance to change your mind and pick another cup if you wish.
Q: should you change your mind and pick another cup? or does it not matter?