1. A bouncy ball vending machine can dispense N small balls in two baskets. The
ID: 3066895 • Letter: 1
Question
1. A bouncy ball vending machine can dispense N small balls in two baskets. The probability for a ball to fall in the left basket is p1, and the probability to fall into the right basket is p2, with p1 + p2 = 1. (a) What is the probability of configuration with n1 balls on the left and n2 balls on the right, with n1 + n2 = N? (b) What is the most probable configuration? (Assume N, n1, n2 >> 1. ) (c) Considering all the possible ball distributions as an ensemble, what is the ensemble averaged number of balls in each basket, <n1>, <n2> ? (d) What are the mean square deviations from those averages.
Explanation / Answer
a) (p1)^n1*(p2)^n2
b)The most probable configuration is p1/p2=n1/n2
c)Average number of balls in the basket <n1> is p1*N and the average number of balls in the basket <n2> p2*N
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