# Statistical Probability of a Deck of Cards

1) Consider a regular deck of cards where the cards ace, jack, queen, and king are numbered 1, 11, 12, and 13 respectively. Consider the experiment of drawing two cards randomly from this deck without replacement.

a. Describe the outcomes of this experiment. List the elements of the sample space.

b. What is the probability of obtaining a total of 6 for the two cards?

c. Let A be the event "total card value is 4 or less". Find P(A) and P(Ac).

2) A regular six faced die is rolled 100 times, leading to the following frequencies.

Number Frequency

1 20

2 16

3 18

4 10

5 14

6 22

a. What is the probability of getting the number 2?

b. What is the probability of getting a number greater than 4?

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#### Solution Preview

1. a) We'll denote the outcomes of the two trials as ordered pairs (a,b), where a represents the number on the first card and b represents the number on the second card.

The total list of possibilities is:

(1,1), (1,2), (1,3)... (1, 13)

(2,1), (2,2), ... (2,13)

...

(13,1), (13,2), ..., (13,13)

There are 13^2 = 169 elements in the sample space!

b) The only ways to get a total of six are the following:

(1,5), ...

#### Solution Summary

The statistical probability of a deck of cards are determined.