Problem 2. Suppose you have a 6-sided die which is weighted, so that the probability of rolling a '6' is 1/2 (and the other 5 sides of the die have probability 1/10). You roll this die 2 times. Let's define the following events. 1. E₁ is the event that exactly one roll is a '6'. 2. E₂ is the event that the difference between the two rolls is an even number. 3. E3 is the event that both rolls are odd numbers. Please answer the following. (a) What is the cardinality and probability of the event E₁? In notation, calculate |E₁| and P(E₁). (b) What is the cardinality and probability of the event E₁ E₂? In notation, calculate |E₁ E₂] and P(E₁ E₂). (c) What is the cardinality and probability of the event E₁ UE3? In notation, calculate |E₁ U E3 and P(E₁ UE3).
Problem 2. Suppose you have a 6-sided die which is weighted, so that the probability of rolling a '6' is 1/2 (and the other 5 sides of the die have probability 1/10). You roll this die 2 times. Let's define the following events. 1. E₁ is the event that exactly one roll is a '6'. 2. E₂ is the event that the difference between the two rolls is an even number. 3. E3 is the event that both rolls are odd numbers. Please answer the following. (a) What is the cardinality and probability of the event E₁? In notation, calculate |E₁| and P(E₁). (b) What is the cardinality and probability of the event E₁ E₂? In notation, calculate |E₁ E₂] and P(E₁ E₂). (c) What is the cardinality and probability of the event E₁ UE3? In notation, calculate |E₁ U E3 and P(E₁ UE3).
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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Transcribed Image Text:Problem 2. Suppose you have a 6-sided die which is weighted, so that the probability of rolling a '6' is
1/2 (and the other 5 sides of the die have probability 1/10). You roll this die 2 times.
Let's define the following events.
1. E₁ is the event that exactly one roll is a '6'.
2. E₂ is the event that the difference between the two rolls is an even number.
3. E3 is the event that both rolls are odd numbers.
Please answer the following.
(a) What is the cardinality and probability of the event E₁? In notation, calculate |E₁| and P(E₁).
(b) What is the cardinality and probability of the event E₁ E₂? In notation, calculate E₁ E₂ and
P(E₁ E₂).
(c) What is the cardinality and probability of the event E₁ UE3? In notation, calculate E₁ U E3 and
P(E₁ U E3).
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