# Sets and Events

1. May 16, 2012

### knowLittle

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.

Last edited: May 16, 2012
2. May 16, 2012

### micromass

Staff Emeritus
(1,1) is in $E\cup F$. If the book says it is not, then the book is wrong.

3. May 16, 2012

### knowLittle

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.