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Two dice are rolled in a random experiment. (a) What is the probability that at most one is a six? (b) If the two faces are different, what is the probability that at most one is a six?

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

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1. Two dice are rolled in a random experiment.
(a) What is the probability that at most one is a six?
(b) If the two faces are different, what is the probability that at most one is a six?

Expert Solution

Step 1

We have given, two dies are rolled in the random experiment.

The sample space is written as,

$Ω = \{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)\}$

The total number of possible cases are $n (Ω) = 36$

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