Empirical & Theoretical Probability Terms of Use    Contact Person: Donna Roberts

 Empirical probability can be thought of as the most accurate scientific "guess" based on the results of experiments to collect data about an event.
 Theoretical probability is the ratio of the number of ways the event can occur to the total number of possibilities in the sample space.

1.
During an experiment, a fair die is tossed. The results appear in the table shown.

a) Based on this data, what is the empirical probability of tossing a 2?
Choose:
 4/15 1/6 1/5 1/30

b) What is the theoretical probability of tossing a 2?
Choose:
 4/15 1/6 1/5 1/30

2.
Using a standard deck of 52 playing cards, a student randomly selects a card, records the suit of the card, and returns the card to the deck. This process is repeated 40 times.

a) Based on this data, what is the empirical probability of selecting a diamond?
Choose:
 1/5 1/8 13/52 1/13
 Suit Frequency Hearts ♥ 12 Diamonds ♦ 8 Spades ♠ 9 Clubs ♣ 11
There are 13 cards
of each suit in a deck of playing cards.

b)
What is the theoretical probability of selecting a diamond?
Choose:
 1/5 1/4 1/8 1/13

3.
A fair coin is tossed 50 times and the results were recorded.

a) Based on this data, what is the empirical probability of tossing a head?
Choose:
 44% 50% 56% 28%
 Suit Frequency Heads 28 Tails 22

b)
What is the theoretical probability of tossing a head?
Choose:
 44% 50% 56% 60%

4.
Three blue, four green and two red chips are in a sack. The chips are drawn at random, recorded, and replaced in the sack.
Eric repeats this process 40 times.

a) Based on this data, what is the empirical probability of drawing a blue chip?
Choose:
 1/3 1/4 2/3 2/5
 Color Frequency Blue 16 Green 15 Red 9

b)
What is the theoretical probability of drawing a blue chip?
Choose:
 1/3 1/4 2/3 2/5

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