July 8th, 2019, 05:55 AM  #1 
Newbie Joined: Jun 2019 From: Melbourne Posts: 4 Thanks: 0  Probability
If a man has 15 balls in his left pocket and 12 balls in his right pocket and repeatedly grabs either box at random to take a ball out, what is the probability that he gets to a point where he has 10 balls in each pocket?

July 8th, 2019, 01:54 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,822 Thanks: 723 
Assuming each pocket equally likely to be chosen, the question becomes: after choosing 7 balls, what is the probability that he has chosen 5 balls from the left and 2 balls from the right. The answer is the binomial term $\frac{1}{2^7}\binom{7}{5}=0.1640625$.


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