Probability Project

Pick a Card....Not Just Any Card!

__Materials:__

Obtain a standard deck of 52 playing cards like those used for bridge, poker, or
solitaire. An experiment will consist of drawing one card at random from
the deck of cards and recording which card was observed. This random
drawing will be simulated by shuffling the deck thoroughly and observing the top
card. Consider the following two events:

A: {card observed is a HEART}

B: {card observed is a face card ie, ACE, KING, QUEEN, or JACK}

Record your findings for these questions in a systematic
scheme...

Write your comments to the final questions and summarize the project...

Prepare a cover sheet with project title, your name and date. (No report
cover is required)

a) Find P(A), P(B), P (A and B), P (A or B)

b) Conduct the experiment 10 times and record the observed card each time.
Be sure to return the observed card each time and thoroughly shuffle the deck
before making the draw. After you have observed 10 cards, calculate the
proportion of observations that satisfy event A, event B, event A and B, and
event A or B. Compare the observed proportions with the true probabilities
calculated in part a.

c) Conduct the experiment 40 more times to obtain a total of 50 observed
cards. Now calculate the proportion of observations that satisfy event A,
event B, event A and B, and event A or B. Compare these proportions with
those found in part b and the true probabilities found in part a.

d) Conduct the experiment 50 more times to obtain a total of 100
observations. Compare the observed proportions for the 100 trials with
those found previously.

What comments do you have concerning the different proportions found in parts b,
c, and d as compared to the true probabilities found in part a? How do you
think the observed proportions and true probabilities would compare if the
experiment were conducted 1,000 times? 1 million times?