BINOMIAL

An Example Of Experimental Probabilities

Five pennies are tossed 4096 times and each time a tally of how many heads and tails ended faceing upward.
The results might look like:

    5 heads and 0 tails appeared 121 times.     Experimental Probability = 121/4096 = 0.02954
    4 heads and 1 Tail happened 638 times.     Experimental Probability = 638/4096 = 0.15576
    3 heads and 2 tails came up 1285 times.     Experimental Probability = 1285/4096 = 0.31370
    2 heads and 3 tails turned up 1293 times.   Experimental Probability = 1293/4096 = 0.31567
    1 head and 4 tails faced up 633 times.        Experimental Probability = 633/4096 = 0.15454
    0 heads and 4 tails appeared 126 times.      Experimental Probability = 126/4096 = 0.03076

Question I.   Calculate the Theoretical Probabilities that correspond to your Experimental Probabilities given the conditions listed above.

An Example Of Theoretical Probabilities

USE:

WITH:

THE RESULTS ARE:

THEN:

Theoretical Probabilities:

Question II.   Make a bar graph with both experimental probabilities and theoretical probabilities. Scale one inch wide bars and let 2 inches represent 0.1 probability units. One tenth inch ruled graph paper is the best to use this time.

Question III.   Write about these theoretical probabilities and experimental probabilities. Find and use some way to tell how close these probabilities are to each other.

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William V. Thayer, PedLog

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