Some probability

Some elementary probability distributions and combinatorics, just for fun. I made up these questions now.
I have an archangel card deck of 40 archangels. They are broken down into 17 colour rays as follows:
Black: 2
Brown: 3
Red: 3
Pink: 3
Orange: 3
Yellow: 2
Green: 2
Turquoise: 2
Blue: 3
Purple: 2
Violet: 2
White: 2
Silver: 1
Gold: 4
Platinum: 1
Rainbow: 2
Diamond: 3
There are 16 female archangels, 21 males and 3 androgynous or twinned angels.
Warm-up (very easy)
Question 1
1. If I do a daily reading of 7 archangels, what is the probability of drawing all female archangels?
2. What is the probability of drawing at least 5 females?
3. What is the probability of drawing all the yellow ray archangels in my seven card draw?
4. What is the probability of drawing the black, diamond, and green ray archangels?

If you can do question 1, then attempt question 2.
Question 2 (easy)
1. What is the probability of getting at least 3 males (out of 7 cards) on all seven days of one week?
2. What is the expected value of days when at least 3 males are drawn over one week?


Question 3 (moderate)

1. If the goal is to draw all the black ray archangels, what is the expected number of failures before the first success?
2. What is the probability of getting 5 failures before 2 successes?
3. What is the expected number of failures before 2 successes?
4. What is the probability of getting at least 4 failures before 3 successes?

All these questions are first half of first year level mathematical statistics.

Edit: This forum seems dead, so it might be that nobody answers these questions, and that's OK.

@Ashiitaka
Come on, guys! Qianlong just wants to have some fun.

(Joke)

Well this is a name I haven't seen in a while!

@Ashiitaka said
Some elementary probability distributions and combinatorics, just for fun. I made up these questions now.
I have an archangel card deck of 40 archangels. They are broken down into 17 colour rays as follows:
Black: 2
Brown: 3
Red: 3
Pink: 3
Orange: 3
Yellow: 2
Green: 2
Turquoise: 2
Blue: 3
Purple: 2
Violet: 2
White: 2
Silver: 1
Gold: 4
Platinum: 1
Rainbow: ...[text shortened]... .

Edit: This forum seems dead, so it might be that nobody answers these questions, and that's OK.

@Ashiitaka said
Some elementary probability distributions and combinatorics, just for fun. I made up these questions now.
I have an archangel card deck of 40 archangels. They are broken down into 17 colour rays as follows:
Black: 2
Brown: 3
Red: 3
Pink: 3
Orange: 3
Yellow: 2
Green: 2
Turquoise: 2
Blue: 3
Purple: 2
Violet: 2
White: 2
Silver: 1
Gold: 4
Platinum: 1
Rainbow: ...[text shortened]... .

Edit: This forum seems dead, so it might be that nobody answers these questions, and that's OK.