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).
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section: Chapter Questions
Problem 14T: An unbalanced coin is weighted so that the probability of heads is 0.55. The coin is tossed ten...
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![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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F423822cb-5d3f-48f4-83a4-f0ba428ae79c%2F4b6f7480-af54-4115-82d1-87da261d618e%2Fyv5kv7e_processed.png&w=3840&q=75)
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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