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I'm sure this question has been asked before but I couldn't find an answer.

There are 8 balls: 3 red, 2 blue and 3 black. Whats the probability of choosing at least 2 red balls if we pick 5 balls?

I would like to know the answer and how to solve those problems.

Thank you.

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Think about the event. This can be done in two ways basically. Choosing 2 red or 3 red.

2 red: You can choose these in $\binom{3}{2}=3$ ways. You are left with 3 balls to choose from the other 5, there are $\binom{5}{3}=10$ ways to do this. So 30 ways in total.

3 red: You have to pick all red ones (there is only one way to do it). $\binom{5}{2}= 10$ ways to choose the rest.

Ok, now you need to count all possible ways of choosing 5 balls from a pool of 8: this is $\binom{8}{5}=56$.

So the answer is $\frac{10+30}{56}=\frac{40}{56} = 0.71 \cdots$.

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    of course there is only one way to pick 3 red balls out of a pool of 3 red balls, you need to pick them all! if not compute $\binom{3}{3}=1$.2012-11-26