Understanding Two Dice Events: EF, E U F, FG, EF^(c), and EFG

In summary, the problem discusses events related to throwing two dice and their outcomes. The events include E, F, and G, with EF representing the intersection of E and F. The solution provided in the book does not include (1,1) in E U F, but the person questioning the solution argues that it should be included. They express frustration with textbooks containing typos and incorrect information.
  • #1
knowLittle
312
3
I have a problem that is suppose to be very basic, but it's hard for me to understand.

Problem:
Two dice are thrown. Let E be the event that the sum of the dice is odd; let F be the event that at least one of the dice lands on 1; and let G be the event that the sum is 5. Describe the events EF, E U F, FG, EF^(c), and EFG.
Note that EF means intersection of the two.

My problem is in E U F.
Why isn't it (1,1) considered? Doesn't it fulfill the requirements of either the sum of dice is odd OR at least one dice lands on a 1?
Namely, that one dice lands on a 1.

The solution from the book is:
S={ (1,2), (1,4), (1,6) ,( 2,1 ) , (4,1) , (6,1) , (2,3) ,(2,5) ,(3,2) , (3,4) ,(3,6 ) ,(4,3) , (4,5) , (5,2) , (5,4) , (5,6) , (6,3),(6,5) } Thank you.
 
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  • #2
(1,1) is in [itex]E\cup F[/itex]. If the book says it is not, then the book is wrong.
 
  • #3
Thank you. It's very annoying to have books like this. My Introduction to Probability and Statistics is filled with typos. It's horrible to be introduced to Probability with textbooks like this.
 

FAQ: Understanding Two Dice Events: EF, E U F, FG, EF^(c), and EFG

1. What is the meaning of EF in two dice events?

EF in two dice events refers to the event where the first dice lands on one of the numbers in the set E, and the second dice lands on one of the numbers in the set F. Essentially, it represents the intersection of events E and F.

2. What is the difference between E U F and EF in two dice events?

E U F represents the union of events E and F, meaning either event E or event F can occur. On the other hand, EF represents the intersection of events E and F, meaning both events must occur simultaneously.

3. How is FG different from EF in two dice events?

FG refers to the event where the first dice lands on one of the numbers in the set F, and the second dice lands on one of the numbers in the set G. This is different from EF because the numbers in set E are not considered in this event. Essentially, it represents the intersection of events F and G.

4. What is the meaning of EF^(c) in two dice events?

EF^(c) represents the complement of event EF, meaning the event where EF does not occur. In other words, either the first dice does not land on one of the numbers in set E, or the second dice does not land on one of the numbers in set F.

5. What does EFG represent in two dice events?

EFG represents the event where all three dice land on one of the numbers in the sets E, F, and G. This is known as the intersection of events E, F, and G, meaning all three events must occur simultaneously.

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