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Theoretical vs Experimental Probability
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Experimental probability: Probability based on a collection of data.
•Will have a table of results or data from the experiment(s)!
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What is the difference between theoretical probability and experimental probability?
• Theoretical probability shows what should happen in an experiment.
• Experimental probability shows what actually happened.
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1. P (heads) =________
2. P (tails) = ________
Jim tossed a coin 35 times. He recorded whether the coin landed on heads or tails. Use the results in the table to find each experimental probability.
HEADS TAILS
llll llll llllllll
llll llll llll
7
3
7
4
35
1535
20
3.What is the theoretical probability of throwing heads?
4. tails?
2
1
2
1
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5. What is the difference between the experimental probability of throwing heads and the theoretical probability of throwing heads? (write answer as a percent rounded to the nearest whole percent)
2
1
7
4
14
1
14
7
14
8
Experimental - theoretical
This is about 7%
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6. What is the difference between the experimental probability of throwing tails and the theoretical probability of throwing tails? (write answer as a percent rounded to the nearest whole percent)
7
3
2
1
14
1
14
6
14
7
Theoretical - Experimental
This is about 7%
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Mrs. Smith has a bag that contains 6 red Lifesavers, 5 yellow Lifesavers, 8 orange Lifesavers and 9 white Lifesavers. She has another bag that contains 3 Butterfingers, 6 Snickers, and 4 Hershey Bars. You are a student that is being rewarded for good behavior so you get to draw a piece of candy from each bag. Find the following probabilities.
Lifesavers
6-red
5 yellow
8 orange
9 white
Candy Bars
3-Butterfingers
6 Snickers
4 Hershey Bars
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Lifesavers
6-red
5 yellow
8 orange
9 white
Candy Bars
3-Butterfingers
6 Snickers
4 Hershey Bars
7.P(yellow Lifesaver, a Snickers)
8.P(red or orange Lifesaver, a Hershey Bar)
9. P(no white lifesaver, a Butterfinger)
13
4
28
86
%813
6
28
5
13
4
28
14
182
15
57
36416%
13
3
28
19
13
3
28
658
%1513
2
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David rolled a number cube, with the numbers 1-6 on it. He recorded the results in the table below.
Number Outcomes
1 IIII2 III3 IIII4 IIII I5 II6 I
Find the THEORETICAL probabilites:
10) P(4) = ______________
11) P(odd number) = __________
12) P(2 or 5) = __________
13) P(a factor of 3) = _________
14) What is the difference between the experimental probability of rolling a 2 or 5, and the theoretical probability of rolling a 2 or 5?
1/6½
1/3
1/3
1/3 – 1/4 = 1/12