Answer to Question #176409 in Statistics and Probability for Aether Sky

Question

Two card are drawn from a deck. How many possible values can each of the following variables take?

1. Sum of the numbers on the card

2. Number of times both cards are black

3. Number of times both cards 7s

4. Number of times the first card is six and the second card is red

5. Number of times the first card is face card and the second card is not a face card.

Answer 1

1.

$N=19$ ; from 2 to 20

2.There are 26 black cards in a deck.

$N=C^2_{26}=\frac{26!}{2!24!}=325$

3.There are 4 7s in a deck.

$N=C^2_4=\frac{4!}{2!2!}=6$

4.There are 4 6s and 26 red cards in a deck.

$N=4\cdot26=104$

5.There are 12 face cards and 40 not face cards in a deck.

$N=12\cdot40=480$