
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 25th, 2017, 07:05 PM  #1 
Member Joined: Apr 2017 From: PA Posts: 45 Thanks: 0  Find the expected value
A box contains two gold balls and three silver balls. You are allowed to choose successively balls from the box at random. You win 1 dollar each time you draw a gold ball and lose 1 dollar each time you draw a silver ball. After a draw, the ball is not replaced. Show that, if you draw until you are ahead by 1 dollar or until there are no more gold balls, this is a favorable uegame. for this, I thought about summing up 1 (2/5)1 (3/2). Then I took a scenario of if I already picked a gold ball. So by then I would sum up 1 (1/4)(3/4). Then, I took anther scenario that we already took a silver ball, so we would have 1 (1/2)1 (1/2). Then, I took another secenario if I took out 2 silver balls to sum up 1 (2/3)(1/3). How would to find the correct expected value? 
June 16th, 2017, 12:35 PM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
Let's list out the possible outcomes, the gain from each, and the probability of each: G: 1, 2/5 SGG: 1, 3/5 * 1/2 * 1/3 = 1/10 SGSG: 0, 3/5 * 1/2 * 2/3 * 1/2 = 1/10 SGSSG: 1, 3/5 * 1/2 * 2/3 * 1/2 = 1/10 SSGG: 0, 3/5 * 1/2 * 2/3 * 1/2 = 1/10 SSGSG: 1, 3/5 * 1/2 * 2/3 * 1/2 = 1/10 SSSGG: 1, 3/5 * 1/2 * 1/3 = 1/10 So the expected value is 1 * (2/5 + 1/10)  1 * (1/10*3) = 0.2 > 0. 

Tags 
expected, find 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Two colored balls, drawing with and without replacement. Find expected number.  beesee  Probability and Statistics  1  June 5th, 2016 09:54 AM 
Expected Value  Kayyne  Probability and Statistics  2  April 13th, 2016 05:13 AM 
find the expected number  450081592  Advanced Statistics  0  November 25th, 2011 09:16 PM 
Expected Value  pskye  Algebra  0  April 4th, 2011 05:50 PM 
find expected value, standard deviation, and probability  jd254  Algebra  0  May 7th, 2009 01:46 AM 