1. ## Probability

An experiment consists of rolling one die. Let A be event that the die shows more than one, B be event that the die shows more than 4, and C be event that die shows an even number.
a)List the sample space of this experiment.

b)Find P(A), P(B), P(C)

c)Find P(A or C), P(A or B), P(A and C), P(B and C)

2. We need to assume that this is a fair die, otherwise we cannot proceed.

$\displaystyle S=\{1,2,3,4,5,6\}$

$\displaystyle A=\{2,3,4,5,6\}$ so P(A)=5/6

$\displaystyle B=\{5,6\}$ so P(B)=1/3

$\displaystyle C=\{2,4,6\}$ so P(C)=1/2

$\displaystyle A\cup C=A=\{2,3,4,5,6\}$ so $\displaystyle P(A\cup C)=5/6$

$\displaystyle AC=C=\{2,4,6\}$ so $\displaystyle P(AC)=1/2$

For A and C to be independent you need $\displaystyle P(AC)=P(A)P(C)$, is that true?

3. I'm not really sure...this is the example I got from my instructor:

Independent variable means the occurrence of one event makes it neither more nor less probable that the other occurs.

The event of getting a 6 the first time a die is rolled and the event of getting a 6 the second time are independent.

By contrast, the event of getting a 6 the first time a die is rolled and the event that the sum of the numbers seen on the first and second trials is 8 are dependent

4. You're not sure of what I've written or what you think the definition of independence is?

The three equivalent definitions are...

$\displaystyle P(AB)=P(A)P(B)$

$\displaystyle P(A|B)=P(A)$

$\displaystyle P(B|A)=P(B)$