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.)

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.)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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