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!)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 35E

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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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