What is the probability of drawing 2 Queens/2 Number cards/at least 1 face card?

[sotnasnab]

In the following exercise, a standard deck of cards is split into 2:

• Deck D1 contains all face cards (4 Jacks, 4 Queens and 4 Kings, a total of 12 cards),
• Deck D2 contains all number cards (4 Aces, 4 Twos, ⋯ and 4 Tens, a total of 40 cards

We roll two fair dice. If the number from the two dice added up is >2, we then draw two cards from D1 (without replacement), otherwise we draw one card from D1 and one card from D2.

a) What is the probability of drawing 2 Queens?
b) What is the probability of drawing 2 number cards?
c) What is the probability of drawing at least 1 face card?

 

[R.M.]

You've got some conditional probabilities going on here. I'd suggest a tree diagram to explore the various possibilities. May help you visualize things a little better.

 

[Steven G]

Part a hint.
What is the probability that you draw your two cards from D1? What is the probability that you then draw two queens?
What is the probability that you draw you draw one card from each of D1 and D2? What is the probability that you then draw two queens?

 

[pka]

In the following exercise, a standard deck of cards is split into 2:

• Deck D1 contains all face cards (4 Jacks, 4 Queens and 4 Kings, a total of 12 cards),
• Deck D2 contains all number cards (4 Aces, 4 Twos, ⋯ and 4 Tens, a total of 40 cards

We roll two fair dice. If the number from the two dice added up is >2, we then draw two cards from D1 (without replacement), otherwise we draw one card from D1 and one card from D2.

a) What is the probability of drawing 2 Queens?
b) What is the probability of drawing 2 number cards?
c) What is the probability of drawing at least 1 face card?

To sotnasnan & R.M. I must wonder if either of you fully understand the setup here.
Let's see. Say that we roll two fair dice & two numbers added up is >2, we then draw two cards from [imath]\mathcal{D}_1[/imath]
The probability that those two numbers added is greater than two is [imath]\dfrac{35}{36}[/imath].
Please follow the posting guidelines and explain that to us.
Drawing two cards from [imath]\mathcal{D}_1[/imath], what is the probability they are both Queens?
Now tell us what otherwise we draw one card from [imath]\mathcal{D}_1[/imath] and one card from [imath]\mathcal{D}_2[/imath]. Really means.

[imath][/imath][imath][/imath][imath][/imath]