The Solitaire Problem

Dr. Lambert - Rsch 6110 - UNC Charlotte

1.  Open the Solitaire game on your computer. Record the number of red and black cards represented by the first five cards that are dealt face up. Repeat this process 50 times. You can simply click on Game and then Deal to be given a fresh sample.

2.  Determine the frequency of each of the possible outcomes in your sample (0,1,2,3,4 or 5 red cards and 0,1,2,3,4 or 5 black cards). Create histograms for the frequency distributions of the number of red and black cards in a trial.

3.  How often did you obtain at least 3 red cards? At least 3 black cards?

4.  Plot the theoretical sampling distribution of the number of red cards in a trial, given fifty trials and that the conditions of a Bernoulli trial have been met.

5.  Using your answer to #4, how often would you expect to obtain at least 3 red cards? At least 3 black cards?

6.  Do the conditions of this simulation meet the conditions for a Bernoulli trial? Why or why not?

7.  Do your simulation results differ from your answer to #4? If yes, explain any differences you observe.

8.  How many possible sequences of red and black cards are there given trials of five cards?

9.  What are all the possible sequences of red and black cards? (RRBRR, etc.)

10.  Use you answers to #8 and #9 to plot the expected frequency distribution of the number of red cards given 32 trials of five cards.

11.  How does this distribution compare to your answers to #2 and #4?

12.  Which one of the following outcomes, given the conditions of a Bernoulli trial are met, is least likely?

a.  BBRBR

b.  BRRRR

c.  RRRRR

d.  BBBBR

e.  All are equally likely.

13.  Which one of the following outcomes, given the conditions of a Bernoulli trial are met, is most likely?

a.  BBRBR

b.  BRRRR

c.  RRRRR

d.  BBBBR

e.  All are equally likely.

14.  Given a large number of trials of five cards, and given the conditions of a Bernoulli trial are met, which of the following outcomes is least likely?

a.  5 red cards

b.  4 red cards

c.  3 red cards

d.  2 red cards

e.  All are equally likely.