Explanation Given Information: Out of three sisters Alice, Betty and Carol the best tennis player is Betty while the Carol and Alice plays at the same level. Alice defeats Carol 50 % of the time. Alice defeats Betty 40 % of the time. Consider the statement from the problem, In order to win $ 100 reward the Alice needs to win two consecutive games against her two sisters. The probability of Alice winning against Carol is, Pr ( A C ) = 50 % = 0.5 . The probability of Alice not winning against Carol is, Pr ( A C ' ) = 1 − Pr ( A C ) = 1 − 0.5 = 0.5 . The probability of Alice winning against Betty is, Pr ( A B ) = 40 % = 0.4 . The probability of Alice not winning against Betty is, Pr ( A B ' ) = 1 − Pr ( A B ) = 1 − 0.4 = 0.6 . The possible combination to win two consecutive games against the given opponents is: WWW, WWL, LWW The provided events are independent to each other, so calculate their probability as, Pr ( E ∩ F ) = Pr ( E ) ⋅ Pr ( F ) For the sequence CBC: Pr ( 2 Wins by using C B C ) = ( .5 ) ( .4 ) ( .5 ) + ( .5 ) ( .4 ) ( .5 ) + ( .5 ) ( .4 ) ( .5 ) = .1 + .1 + .1 = .3 For the sequence BCB: Pr ( 2 Wins by using B C B ) = (

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

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Chapter 6, Problem 4P

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The sequence Alice should choose if Alice’s mother give her $100 when she can win two consecutive games against her two sisters such that out of three sisters Alice, Betty and Carol.

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Chapter 6 Solutions

Finite Mathematics & Its Applications (12th Edition)

Ch. 6.1 - 1. Lightbulbs A machine produces lightbulbs. As...Ch. 6.1 - 2. Citrus Fruit Suppose that there are two crates...Ch. 6.1 - 1. Committee Selection A committee of two people...Ch. 6.1 - 2. Selecting Letters A letter is selected at...Ch. 6.1 - Heads and Tails An experiment consists of tossing...Ch. 6.1 - Four-Sided Dice A pair of four-sided dice-each...Ch. 6.1 - 5. Selecting from Urns Suppose that we have two...Ch. 6.1 - Coin Tosses An experiment consists of tossing a...Ch. 6.1 - 7. Efficiency Studies An efficiency expert records...Ch. 6.1 - Census Data A census taker records the annual...

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The sequence Alice should choose if Alice’s mother give her $ 100 when she can win two consecutive games against her two sisters such that out of three sisters Alice, Betty and Carol.

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The sequence Alice should choose if Alice’s mother give her $100 when she can win two consecutive games against her two sisters such that out of three sisters Alice, Betty and Carol.

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