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 Probability and Statistics Basic Probability and Statistics Math Forum

 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. Tags conditional, probability Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Jaket1 Probability and Statistics 1 January 29th, 2017 08:19 AM Lawrence303 Probability and Statistics 0 December 21st, 2014 11:35 PM theunique123 Probability and Statistics 1 October 11th, 2014 12:49 PM dbullock28 Advanced Statistics 1 July 26th, 2013 06:34 PM chapsticks Advanced Statistics 1 September 18th, 2012 03:24 PM

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