( A ) Explanation Calculation: Consider urn U 1 that contains 2 white balls and 3 red balls. Let X be the event of drawing a red ball. Let the expected number of red balls if the first ball is replaced be given by E X . The possible number of ways that ball is selected is given by n X = R R , R W , W R , W W . The value of various events’ outcomes is shown as in the table: Events Number of red balls x e 1 = R R 2 e 2 = R W 1 e 3 = W R 1 e 4 = W W 0 Compute the probability for X = 2 by using the formula, P X = x = Number of x Total number of outcomes , P X = 2 = Number of red balls in first draw Total number of balls × Number of red balls in second draw Total number of balls = 3 5 × 3 5 = 9 25 Compute the probability for X = 1 (event 2nd) by using the formula, P X = x = Number of x Total number of outcomes , P X = 1 = Number of red balls in first draw Total number of balls × Number of White balls in second draw Total number of balls = 3 5 × 2 5 = 6 25 Compute the probability for X = 1 (event 3rd) by using the formula, P X = x = Number of x Total number of outcomes , P X = 1 = Number of white balls in first draw Total number of balls × Number of red balls in second draw Total number of balls = 2 5 × 3 5 = 6 25 Compute the probability for X = 0 < ( B ) To determine To calculate: The expected number of red balls if urn U 1 contains 2 white balls and 3 red balls and two balls are drawn from it in succession in a way such that the first ball drawn is not replaced.

Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

14th Edition

ISBN: 9780134677972

Author: Barnett

Publisher: PEARSON

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Chapter 8, Problem 43RE

( A )

To determine

To calculate:The expected number of red balls if urn U1 contains 2 white balls and 3 red balls and two balls are drawn from it in succession in a way such that the first ball drawn is replaced.

( B )

To determine

To calculate:The expected number of red balls if urn U1 contains 2 white balls and 3 red balls and two balls are drawn from it in succession in a way such that the first ball drawn is not replaced.

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Chapter 8, Problem 42RE

Chapter 8, Problem 44RE

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Chapter 8 Solutions

Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

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The expected number of red balls if urn U 1 contains 2 white balls and 3 red balls and two balls are drawn from it in succession in a way such that the first ball drawn is replaced.

Solution Summary: The author calculates the expected number of red balls if urn U_1 contains 2 white balls and 3 red ball.