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April 10th, 2018, 06:16 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, 11:17 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,201 Thanks: 1156 
let $P[Wk]$ be the probability of picking white in $k$ picks note it's assumed picks are independent of one another. $P[W]=P[W1 ]+P[W2 ]+P[W3 ]+P[W4] = \dfrac 1 5 + \left(\dfrac 4 5\right)\left(\dfrac 1 5\right)+\left(\dfrac 4 5\right)^2\left(\dfrac 1 5\right)+\left(\dfrac 4 5\right)^3\left(\dfrac 1 5\right)=\dfrac{369}{625}$ 
April 10th, 2018, 02:30 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,641 Thanks: 625 
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 1P.


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