Example 2.10.1 There are three dice in a bag. One has one red face, another has two red faces,and the third has three red faces. One of the dice is drawn at random from the bag, each die havingan equal chance of being drawn. The selected die is repeatedly rolled.(a) What is the probability that red shows on the first roll?(b) Given that red shows on the first roll, what is the conditional probability that red shows onthe second roll?(c) Given that red shows on the first three rolls, what is the conditional probability that the selecteddie has red on three faces?

Answered: Image /qna-images/answer/1b18327b-4679-4be0-85cf-bed62a65dd1c.jpg

Answered: Example 2.10.1 There are three dice in…

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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Example 2.10.1 There are three dice in a bag. One has one red face, another has two red faces, and the third has three red faces. One of the dice is drawn at random from the bag, each die having an equal chance of being drawn. The selected die is repeatedly rolled. (a) What is the probability that red shows on the first roll? (b) Given that red shows on the first roll, what is the conditional probability that red shows on the second roll? (c) Given that red shows on the first three rolls, what is the conditional probability that the selected die has red on three faces?
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3. You get a haircut from Barber Shop 1 30% of the time and Barber Shop 2 70% of the time. Barber Shop 1 gives a good haircut 80% of the time and a bad haircut 20% of the time while Barber Shop 2 gives a good haircut 90% of the time and a bad haircut 10% of the time. For any given haircut, the probability that it is a bad haircut from Barber Shop 1 is Barber Shop 2 is and the probability that it is a good haircut from O.06; .63 .2; .73 O.06; .73 .2; .63
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Suppose you roll the dice repeatedly, and you will keep flipping it until you observe two total sixes, and then stop. What is the probability that it takes exactly 4 rolls to get your two sixes?

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