Answered: A bag contains three kinds of dice:…

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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A bag contains three kinds of dice: seven 4-sided dice, three 6-sided dice, and two 12-sided dice. A die is drawn from the bag and then rolled, producing a number. For example, the 12-sided die could be chosen and rolled, producing the number 10. Assume that each die is equally likely to be drawn from the bag.

a. What is the probability that the roll gave a six?

b. What is the probability that a 6-sided die was chosen, given that the roll gave a six.

Expert Solution

Step 1

Let X: the number obtained is 6

A: A four sided dice is drawn

B: A six sided dice is drawn

C: A twelve sided dice is drawn

We know,

$P (A) = \frac{7}{12} P (B) = \frac{3}{12} P (C) = \frac{2}{12}$

And

$P (X | A) = 0 P (X | B) = \frac{1}{6} P (X | C) = \frac{1}{12}$

Using Law of Total Probability,

$P (X) = P (X | A) \times P (A) + P (X | B) \times P (B) + P (X | C) \times P (C) = 0 + \frac{1}{6} \times \frac{3}{12} + \frac{1}{12} \times \frac{2}{12} = \frac{1}{18}$

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