Suppose a jar contains 8 balls among which 5 are red and 3 are blue. If i pick, 3 balls from this jar, what is the probability that "exactly" two of them are blue ball?
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$\begingroup$ If you are picking without replacement (which is the natural interpretation, I think) then neither is correct. $\endgroup$– André NicolasSep 12, 2015 at 20:00
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1 Answer
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The total number of ways to choose $3$ out of $8$ balls is $\binom83=56$
The number of ways to choose $2$ out of $3$ blue balls and $1$ out of $5$ red balls is $\binom32\cdot\binom51=15$
Hence the probability is $\dfrac{15}{56}$
answered Sep 12, 2015 at 20:01
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$\begingroup$ are you assuming that the balls are unique? Whats the answer if the balls of a certain color are alike? $\endgroup$ Sep 12, 2015 at 20:10
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$\begingroup$ @karthikts: It doesn't make any difference. There are $56$ (not necessarily different) ways to choose $3$ out of $8$, and $15$ of them contain exactly two blue. $\endgroup$ Sep 12, 2015 at 20:29
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$\begingroup$ Got it! .. Considering this is executed without replacement .... Your answer is same as 3/8*2/7*5/6 + 3/8*5/7*2/6 + 5/8*3/7*2/6 $\endgroup$ Sep 13, 2015 at 15:30