My Math Forum Conditional probability

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 April 10th, 2018, 05:16 AM #1 Newbie   Joined: Apr 2018 From: United Kingdom Posts: 1 Thanks: 0 Conditional probability I hope someone can help! My problem is an analogy of a work question and I canâ€™t solve it for the life of me ðŸ™ˆ â€¢ You have a bag of 10 marbles â€¢ 8 are black â€¢ 2 are white â€¢ You select a marble â€¢ If it is black, you put the marble back and pick again â€¢ If it is white you stop selecting â€¢ After a maximum of 4 selections, what is the probability that you will have selected a white? Any help would be very much appreciated!!
 April 10th, 2018, 10:17 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,382 Thanks: 1281 let $P[W|k]$ be the probability of picking white in $k$ picks note it's assumed picks are independent of one another. $P[W]=P[W|1 ]+P[W|2 ]+P[W|3 ]+P[W|4] = \dfrac 1 5 + \left(\dfrac 4 5\right)\left(\dfrac 1 5\right)+\left(\dfrac 4 5\right)^2\left(\dfrac 1 5\right)+\left(\dfrac 4 5\right)^3\left(\dfrac 1 5\right)=\dfrac{369}{625}$
 April 10th, 2018, 01:30 PM #3 Global Moderator   Joined: May 2007 Posts: 6,710 Thanks: 675 It is easy to compute the probability of P, a black being selected each time, since you are putting it back each time. P$=(\frac{4}{5})^4$. So the probability that a white had been selected is 1-P.

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