In a bag there are 3 six-sided dice. Two of the dice have faces marked 1, 2, 3, 4, 5, 6.The other is a special die with faces marked 1, 2, 3, 5, 5, 5..One die is randomly selected and tossed.(a) What is the probability that the die shows a 5?4***D(b) Given that the die shows a 5, what is the probability that it is the special die?

Answered: One die is randomly selected and…

One die is randomly selected and tossed. (a) What is the probability that the die shows a 5? A (b) Given that the die shows a 5, what is the probability that it is the special die?

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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Question

In a bag there are 3 six-sided dice. Two of the dice have faces marked 1, 2, 3, 4, 5, 6.
The other is a special die with faces marked 1, 2, 3, 5, 5, 5..
One die is randomly selected and tossed.
(a) What is the probability that the die shows a 5?
4
***D
(b) Given that the die shows a 5, what is the probability that it is the special die?

Expert Solution

Step 1

Let us define some events

A : The die is fair.

B : The die is special.

E : The die shows a 5.

Given that

2 dies are fair and 1 die is apecial, then

P(A) = 2/3 and P(B) = 1/3

P(E|A) = 1/6 since the die is fair.

P(E|B) = 3/6 = 1/2 since special die has 3 faces marked with 5.

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