2. Suppose that a box initially contains b black balls and w white balls. In each step, we select a uniformly random ball from the box, and then put it back together with a new ball of the same color. Let B, be the event that the nth ball selected from the box is black. Note that P(B1) = b/(b+w). Using the Law of Total Probability, show that P(B2) = b/(b+w) and P(B3) = b/(b+w). (In fact, P(B„) =b/(b+w), for any n> 1. You do not need to show this.)

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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2. Suppose that a box initially contains b black balls and w white balls. In each
step, we select a uniformly random ball from the box, and then put it back
together with a new ball of the same color. Let B, be the event that the nth ball
selected from the box is black. Note that P(B1) =b/(b+w). Using the Law
of Total Probability, show that P(B2) = b/(b+w) and P(B3) = b/(b+w).
(In fact, P(B„) =b/(b+w), for any n > 1. You do not need to show this.)
Transcribed Image Text:2. Suppose that a box initially contains b black balls and w white balls. In each step, we select a uniformly random ball from the box, and then put it back together with a new ball of the same color. Let B, be the event that the nth ball selected from the box is black. Note that P(B1) =b/(b+w). Using the Law of Total Probability, show that P(B2) = b/(b+w) and P(B3) = b/(b+w). (In fact, P(B„) =b/(b+w), for any n > 1. You do not need to show this.)
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