Probability of winning a card game

[mkdog19]

A deck of a newly created card game consists of 60 cards. In this deck, there are:
- 4 VB cards
- 4 HBL cards
- 4 DD cards
- 4 SP cards
- 4 CC cards
- 1 RH cards
- 4 FD cards
- 1 WC cards
- 14 LA cards
- Other misc cards

A player draws 7 cards. To win, the player needs to draw:
* 1 VB card, and
* 1 HBL card, and
* 1 DD or SP card, and
* 1 LA card, and
* 1 CC or SP or RH or FD card, and
* 1 SP or WC card

The remaining card(s) can be anything.

(a) What is the probability of winning if 7 cards are drawn?

(b) What is the probability of winning if 8 cards are drawn?

(c) What is the probability of winning if 9 cards are drawn?

What I've tried so far: I don't know how to deal with the SP cards appearing in 3 places. My (wrong math) for 7 cards is:
(4/60)*(4/59)*(4/58+4/58)*(14/57)*(4/56+3/56+1/56+4/56)*(2/55+1/55)*(54/54)*7!
Which gives 0.902%
For 8 cards: (4/60)*(4/59)*(4/58+4/58)*(14/57)*(4/56+3/56+1/56+4/56)*(2/55+1/55)*(54/54)*(53/53)*8!
For 9 cards: multiply the 8-cards probability by 9.

I know I'm wrong because if the player draws 10 cards, the probability of winning would be > 100%. However, a player draws 10 LA cards would lose.

So, I don't know how to solve this problem & need help!

 

[Steven G]

A deck of a newly created card game consists of 60 cards. In this deck, there are:
- 4 VB cards
- 4 HBL cards
- 4 DD cards
- 4 SP cards
- 4 CC cards
- 1 RH cards
- 4 FD cards
- 1 WC cards
- 14 LA cards
- Other misc cards

A player draws 7 cards. To win, the player needs to draw:
* 1 VB card, and
* 1 HBL card, and
* 1 DD or SP card, and
* 1 LA card, and
* 1 CC or SP or RH or FD card, and
* 1 SP or WC card

The remaining card(s) can be anything.

(a) What is the probability of winning if 7 cards are drawn?

(b) What is the probability of winning if 8 cards are drawn?

(c) What is the probability of winning if 9 cards are drawn?

What I've tried so far: I don't know how to deal with the SP cards appearing in 3 places. My (wrong math) for 7 cards is:
(4/60)*(4/59)*(4/58+4/58)*(14/57)*(4/56+3/56+1/56+4/56)*(2/55+1/55)*(54/54)*7!
Which gives 0.902%
For 8 cards: (4/60)*(4/59)*(4/58+4/58)*(14/57)*(4/56+3/56+1/56+4/56)*(2/55+1/55)*(54/54)*(53/53)*8!
For 9 cards: multiply the 8-cards probability by 9.

I know I'm wrong because if the player draws 10 cards, the probability of winning would be > 100%. However, a player draws 10 LA cards would lose.

So, I don't know how to solve this problem & need help!

I don't know how to deal with the SP cards appearing in 3 places. So do two cases- One with SP and one w/o SP. Let's see how far you get with that hint.

 

[pka]

A deck of a newly created card game consists of 60 cards. In this deck, there are:
- 4 VB cards
- 4 HBL cards
- 4 DD cards
- 4 SP cards
- 4 CC cards
- 1 RH cards
- 4 FD cards
- 1 WC cards
- 14 LA cards
- Other misc cards

A player draws 7 cards. To win, the player needs to draw:
* 1 VB card, and
* 1 HBL card, and
* 1 DD or SP card, and
* 1 LA card, and
* 1 CC or SP or RH or FD card, and
* 1 SP or WC card

mkdog19, this is such a poorly worded question as to render it meaningless.
Most important is the phrase "Other misc cards". The list tells us about forty cards.
But the "Other misc cards" do that include any that have bee listed?
Why not just say that those twenty cards are blank? That would fix things clearly.
But again that may not be true if those "Other misc cards" can be repeats.

 

[Denis]

A deck of a newly created card game consists of 60 cards. In this deck, there are:
- 4 VB cards
- 4 HBL cards
- 4 DD cards
- 4 SP cards
- 4 CC cards
- 1 RH cards
- 4 FD cards
- 1 WC cards
- 14 LA cards
- Other misc cards

When you saw this for the 1st time, did you think it was ridiculous?

Seriously, any reason why "da deck" is not showing some organization,
also some simplicity perhaps a bit like:
1: A
1: B
4: C
4: D
4: E
4: F
4: G
4: H
14: I
20: J (or "blanks" as Pka says...)
===
60

 

[mkdog19]

"Other misc cards" are not repeats.

I'm not getting the "One with SP and one w/o SP" hint, because I already incorporated that in the "(4/58+4/58)*...*(4/56+3/56+1/56+4/56)*(2/55+1/55)". If you see obvious errors, I'd appreciate some detailed feedback.

Is this a Hypergeometric Distribution problem? Does anyone here actually know how to solve this problem and can provide some help?