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There's 1 box with 10 balls:

3 white 2 black 5 blue

2 balls are removed the box randomly, and the first one is not replaced.

What is the probability of getting at least 1 white ball?

Here's what I cooked up:

The probability of getting at least 1 white ball equals the sum of the probabilities of getting a white ball first and getting a white ball second. The probability of getting a white ball on the first one is 3/10. The probability of getting a white ball on the second one is 2/9.

So the probability would be:

3/10 + 2/9 = 47/90

I'm solving this on a book which says the answer is 8/15.

So, my answer is 0.52222..., and their answer is 0.5333...

Am I doing anything wrong?

Thanks in advance.

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    If you apply your argument to the case of drawing three balls, each of which is blue, you'd get $95/72$..2012-10-20

3 Answers 3

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Here Question is What is the probability of getting at least 1 white ball ? So there are 3 possible cases as follows

  1. 1st is white AND 2nd is not for that (3/10) * (7/9)

OR 2. 1st is not white AND 2nd is white for that (7/10)*(3/9) (adding dummy characters in order to save the edit)

OR 3. both are white for that (3/10) * (2/9)

for answer add these 3 cases so answer is 48/90 which is 0.533333
In probability questions remember OR means ADD, AND means Multiply

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    Which is precisely why I have given you the advice :). Have a good time. PS: The advice also applies to comments; I'm sure you'll get it soon enough.2012-10-20
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You want to know the probability of "one of the two balls is white" = "the first ball is white OR (the first ball isn't white AND the second ball is white)".

OR is +

AND is $\times$

So you get $\frac{3}{10} + \frac{10-3}{10}\times \frac{3}{10-1}$.

$\frac{3}{10}$ and $\frac{10-3}{10}$ because you have 3 white balls and 10 balls so 10 - 3 not-white balls

$\frac{3}{10-1}$ because when you pick the second ball, you removed one non-white ball

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or you can arrive at the same answer by thinking in reverse. If at least one ball is white, then the only other combination is Non-white in the 1st pick and No-white in the 2nd pick. Then 1-(2 non-white probability)=at least 1 white picked!

So 1st pick for non-white = 7/10 and the 2nd pick for non-white = 6/9. This probability for this combination is 7/10 x 6/9 = 7/15. So the probability of getting at least 1 white = 1-7/15= 8/15 = 0.53333....