2 votes 2 votes A total of n balls are sequentially and randomly chosen, without replacement, from an urn containing r red and b blue balls (n … r + b). Given that k of the n balls are blue, what is the conditional probability that the first ball chosen is blue? Vivek sharma asked Sep 18, 2016 Vivek sharma 30 points 1.5k views answer comment Share See all 0 reply Please log in or register to add a comment.
0 votes 0 votes an urn containing r red and b blue balls So, it can contain rC1 ball or bC1 balls Now, among n balls k balls are blue, (n-k) balls are red So, 1st urn can contain $\frac{kC1*bC1}{kC1*bC1+(n-k)C1*rC1}$ srestha answered Sep 22, 2016 srestha 5.2k points comment Share See all 0 reply Please log in or register to add a comment.
0 votes 0 votes To choose $n$ ball from $(r+b)$ balls can be done in $\binom{r+b}{n}$ now, k ball out of those n chosen balls are guaranteed to be blue, so to make sure that first ball is blue we can choose our first ball from these k balls in $\binom{k}{1}$ and remaining $(n-1)$ ball in $\binom{r+b-k}{n-1}$ ways. $Probability=$$\frac{\binom{k}{1}\binom{r+b-k}{n-1}}{\binom{r+b}{n}}$ bhuv answered Aug 21, 2017 bhuv 30 points comment Share See all 0 reply Please log in or register to add a comment.