Help with Probability & Sample Space Questions

[normaldistribut]

I have been having a time trying to get the answers for these two questions. Can anyone please help me?

1)
Suppose a fair die is tossed and the number showing on the top face is recorded. Let E, F, and G be the following events: E: {1,2,3,5}, F:{2,4}, G:{1,4,6} Compute the probability of the following event: E' U G'

2)
A box contains 12 items, four of which are defective. An item is chosen at random and not replaced. This is continued until all four defective items have been selected. The total number of items selected is recorded. Describe the associated sample space.
A.{1, 2, 3, 4}
B.{5, 7, 9, 11}
C.{3, 6, 9, 12}
D.{4, 5, 6, 7 ,8, 9, 10, 11, 12}

 

[soroban]

Hello, normaldistribut!

1) A fair die is tossed.
Let $$E, F, G$$ be the following events:
.$$E\!:\,\{1,2,3,5\}\quad F\!:\,\{2,4\} \quad G\!:\,\{1,4,6\}$$
Compute the probability of: $$E' \cup G'$$

$$\begin{Bmatrix}E' &=& \{4,6\} \\ G' &=& \{2,3,5\}\end{Bmatrix} \quad\Rightarrow\quad E' \cup G' \;=\;\{2,3,4,5,6\}$$

Therefore: .$$P(E' \cup G') \;=\;\frac{5}{6}$$

2) A box contains 12 items, four of which are defective.
An item is chosen at random and not replaced.
This is continued until all four defective items have been selected.
The total number of items selected is recorded.
Describe the associated sample space.

$$A.\;\{1, 2, 3, 4\} \quad B.\;\{5, 7, 9, 11\} \quad C.\;\{3, 6, 9, 12\}$$
. . . . . . . . $$D.\;\{4, 5, 6, 7 ,8, 9, 10, 11, 12\}$$

Exactly where is your difficulty?
Do you understand the problem?

Can you see that the answer is $$D$$?

 

[normaldistribut]

I am so sorry, the second one wasn't the problem I was having the issues with because I had already answered that and got it right. My question was supposed to be,

A card is selected at random from a standard deck. Let E, F, and G be the following events.
E: The card is black.
F: The card is a diamond.
G: The card is an ace.
Choose the answer that correctly describes E U f' U G
A.The card is black or a diamond or not an ace.
B.The card is black or not a diamond or an ace.
C.The card is black and not a diamond.
D.The card is not a diamond or an ace.

It goes back to the first problem where I am having the trouble with understanding the f' part or any part where there is a top line which throws me off. My apologies.
Thank you so much for your help!