An experiment consists of three fair, different coloured dice being rolled (the dice are 6-sided and the sides show numbers 1, \ldots ,61,…,6). Let AA be the event that none of the dice shows numbers 1 Q3.1 If we denote by SS the sample space of this experiment, what is the size of SS? Q3.2 What is the probability of AA? Q3.3 What is the probability of BB? Q3.4 What is the probability of A\cap BA∩B? Q3.5 Are the events AA and BB independent? (You must justify your answer!)

An experiment consists of three fair, different coloured dice being rolled (the dice are 6-sided and the sides show numbers 1, \ldots ,61,…,6). Let AA be the event that none of the dice shows numbers 1 Q3.1 If we denote by SS the sample space of this experiment, what is the size of SS? Q3.2 What is the probability of AA? Q3.3 What is the probability of BB? Q3.4 What is the probability of A\cap BA∩B? Q3.5 Are the events AA and BB independent? (You must justify your answer!)

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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Q3

Q3.1

If we denote by SS the sample space of this experiment, what is the size of SS?

Q3.2

What is the probability of AA?

Q3.3

What is the probability of BB?

Q3.4

What is the probability of A\cap BA∩B?

Q3.5

Are the events AA and BB independent? (You must justify your answer!)

Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.

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