# Probability question (two draws)

If I draw 2 balls from a bag which contains 2 pink, 3 blue and 4 orange balls, what's the probability that the first ball would be pink and the second blue - as a decimal? Thanks. :)

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Do you want to know the probability to get the second ball blue assuming the first one is pink or assuming that the first one can be of any colour? – Riccardo.Alestra Jul 3 '12 at 13:33
Hi. Assuming the first one is pink. Need the probability that both, the first one would be pink and the second blue. :) Thanks. – Joey Morani Jul 3 '12 at 13:36

## 2 Answers

Hint: what is the chance that you get a pink ball on the first draw? Given that one pink ball is removed (I presume you are drawing without replacement), what is the chance that the second draw is blue? The chance of both is the product. Now you have a fraction to express in decimal. What fraction is it?

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Pink ball removed first would be 2/9. So a blue ball removed after would be 3/8 ? Do I then add them together? – Joey Morani Jul 3 '12 at 13:32
@JoeyMorani: No, as I said, you multiply them. When you have to have two things happen, and the probabilities are independent (we have taken account of the pink ball removal), they are multiplied. It's like flipping a coin three times hoping for three heads. The chance is $(\frac 12)^3=\frac 18$ – Ross Millikan Jul 3 '12 at 13:42
Ah thanks. Got it. I was adding them where I needed to multiply. Thanks again. – Joey Morani Jul 3 '12 at 13:50
You can easily see that adding is wrong, otherwise the odds of tossing three heads in a row would be 3/2.. – Ben Millwood Jul 3 '12 at 15:20
@JoeyMorani: you add when you want either of two events (and you need them to be mutually exclusive). Adding makes it more likely, and two chances are more likely than one. You multiply when you want both of two events (and you need them to be independent). Needing two event must be less likely than either one, and as probabilities are always less than 1, it will work out that way. – Ross Millikan Jul 3 '12 at 16:31

The probability to pick up the first ball pink is $\frac{2}{9}$ that means 0.22. If you don't get the first ball blue, the probability to have the second ball blue is $\frac{3}{8}$ ($0.375$). If the first ball is blue, the probability to have the secon ball of the same colour is: $\frac{1}{4}$ ($0.25$). The probability to pick the first pink and the second blue is in the first case: $\frac{2}{9}\frac{3}{8}$, in the second: $\frac{2}{9}\frac{1}{4}$

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