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Re: The only items on a shelf are 8 green bins and 4 orange bins [#permalink]
4
Carcass wrote:
The only items on a shelf are 8 green bins and 4 orange bins. If 3 bins are to be selected from the shelf, one after the other, at random and without replacement, what is the probability that at least one green bin is selected?

Give your answer as a fraction.

Show: ::
\(\frac{54}{55}\)


We want P(select AT LEAST 1 green bin)

When it comes to probability questions involving "at least," it's best to try using the complement.
That is, P(Event A happening) = 1 - P(Event A not happening)
So, here we get: P(getting at least 1 green bin) = 1 - P(not getting at least 1 green bin)
What does it mean to not get at least 1 green bin? It means getting zero green bins.
So, we can write: P(getting at least 1 green bin) = 1 - P(getting zero green bins)


P(getting zero green bins)
P(getting zero green bins) = P(orange bin 1st AND orange bin 2nd AND orange bin 3rd)
= P(orange bin 1st) x P(orange bin 2nd) x P(orange bin 3rd)
= 4/12 x 3/11 x 2/10
= 1/3 x 3/11 x 1/5
= 1/55

So, P(getting at least 1 green bin) = 1 - 1/55 = 54/55

Answer: 54/55

Cheers,
Brent
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Re: The only items on a shelf are 8 green bins and 4 orange bins [#permalink]
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