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a.i. Find the probability of rolling exactly one red face. a.lii.Find the probability of rolling two or more red faces. b. Show that, after a turn, the probability that Ted adds exactly $10 to his winnings is .

a.i. Find the probability of rolling exactly one red face. a.lii.Find the probability of rolling two or more red faces. b. Show that, after a turn, the probability that Ted adds exactly $10 to his winnings is .

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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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There are three fair six-sided dice. Each die has two green faces, two yellow faces and two red faces.

Question 4 There are three fair six-sided dice. Each die has two green faces, two yellow faces and two red faces. All three dice are rolled. Ted plays a game using these dice. The rules are: • Having a turn means to roll all three dice. • He wins $10 for each green face rolled and adds this to his winnings. • After a turn Ted can either: o end the game (and keep his winnings), or o have another turn (and try to increase his winnings). • If two or more red faces are rolled in a turn, all winninge are loet and the game ende. The random variable D ($) represents how much is added to his winnings after a turn. The following table shows the distribution for D, where Sw represents his winnings in the game so far. D ($) 10 20 30 1 1 P(D=d) y 3 27 a.i. Find the probability of rolling exactly one red face. a.iFind the probability of rolling two or more red faces. b. Show that, after a turn, the probability that Ted adds exactly $10 to his winnings is . c.l. Write down the value of z. C.i.Hence, find the value of y. d. Ted will always have another turn if he expects an increase to his winnings. Find the least value of w for which Ted should end the game instead of having another turn.
Transcribed Image Text:Question 4 There are three fair six-sided dice. Each die has two green faces, two yellow faces and two red faces. All three dice are rolled. Ted plays a game using these dice. The rules are: • Having a turn means to roll all three dice. • He wins $10 for each green face rolled and adds this to his winnings. • After a turn Ted can either: o end the game (and keep his winnings), or o have another turn (and try to increase his winnings). • If two or more red faces are rolled in a turn, all winninge are loet and the game ende. The random variable D ($) represents how much is added to his winnings after a turn. The following table shows the distribution for D, where Sw represents his winnings in the game so far. D ($) 10 20 30 1 1 P(D=d) y 3 27 a.i. Find the probability of rolling exactly one red face. a.iFind the probability of rolling two or more red faces. b. Show that, after a turn, the probability that Ted adds exactly $10 to his winnings is . c.l. Write down the value of z. C.i.Hence, find the value of y. d. Ted will always have another turn if he expects an increase to his winnings. Find the least value of w for which Ted should end the game instead of having another turn.
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