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?