A box has 7 green items and 5 black items. We randomly pick 2 items from the box. What are the odds that both items are green if we know that the first item is green?
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2That's a great question. Can you give us a hint? – John Douma Dec 01 '16 at 03:53
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Conditional probability or rather, Bayes' theorem. – SchrodingersCat Dec 01 '16 at 03:56
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I know the odds of picking a green or a black item but when there is an "if we know ..." part then I get all confused. – user394807 Dec 01 '16 at 03:56
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Hint: if we know the first item is green, what is in the box before the second pick? – David Dec 01 '16 at 03:57
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Then there would be 6 green items and 5 black (11 total). I'm guessing 6/11 = 0.54545454545? That feels too simple to be the right answer somehow. – user394807 Dec 01 '16 at 03:59
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See if you can write down clearly explained reasons. Then you won't need to guess. – David Dec 01 '16 at 04:00
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The probability that both of the picked items are green is $\frac{\binom{6}{1}}{\binom{11}{1}}$. This is because we have already picked one green item by the given condition, thus giving us 6 green items and 11 items remaining in total;out of which we have to pick only one green ball in order for the condition to be satisfied. Thus, the odds in favour of both items being green provided one item picked is already green is 6 to 11.
vidyarthi
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