Answer to Question #175028 in Statistics and Probability for Celle

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

Answer 1

Solution:

(1):

In a deck of 52 cards, there are cards numbered from 1 to 13.

When we draw two cards, least sum obtained is 2 (=1+1) and greatest sum obtained is 26 (=13+13).

(2): Both cards are black.

Spades and clubs are black cards.

So, the following are the possible cases for both black cards:

Thus, total possible values for this variable = 3

(3): Both cards are 7s.

There are four 7s, one in each of spades, clubs, hearts, and diamonds.

So, the following are the possible cases for both 7s cards:

Thus, total possible values for this variable = 6

(4): The first card is 6 and the second card is red.

There are four 6s, one in each of spades, clubs, hearts, and diamonds.

And hearts and diamonds are red cards.

So, the following are the possible cases for first card 6 and second card red:

Thus, total possible values for this variable = 8