Name Class Date Practice
Form G
Experimental and Theoretical Probability
You roll a standard number cube 10 times. The results are shown below.
6, 4, 6, 1, 5, 2, 4, 2, 4, 3
Find the experimental probability of each outcome.
1. P(rolling a 5) 1
2. P(rolling a 6) 1
7
3. P(rolling an even number) 10
1
4. P(rolling a 1) 10
5
10
5. What is the experimental probability of rolling an odd number on a standard
number cube? For 50 rolls of the number cube, predict the number of rolls
that will result in an odd number. 0.3; 15
Find the theoretical probability of each outcome.
6. P(rolling a 5) 1
7. P(rolling a 6) 1
6
6
8. P(rolling an even number) 1
2
10. P(rolling an odd number) 1
2
9. P(rolling a 1) 1
6
11. P(rolling a multiple of 3) 1
3
A bag contains 2 red ping-pong balls, 3 green ping-pong balls, 3 blue ping-pong
balls, and 1 yellow ping-pong ball. Find the probability of randomly selecting
each outcome.
12. P(not red) 7
13. P(not green) 2
14. P(not blue) 2
15. P(not yellow) 8
9
3
3
9
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Name Class Date Practice (continued)
Form G
Experimental and Theoretical Probability
16. A game is played where students throw beanbags at the target
shown to the right. Each region of the target is the same size and
every beanbag hits the target. For one game, section A was hit
6 times, section B 3 times, section C 8 times, and section D 5 times.
A
C
a. What is the experimental probability of hitting section D? 5
B
22
b. What is the theoretical probability of hitting section D? 1
4
17. Reasoning How are the probability of an event and the probability of its
complement related mathematically? Their sum is equal to 1.
Two standard number cubes are rolled. Find each probability.
18. P(a sum equal to 2) 1
19. P(sum not equal to 2) 35
36
36
20. P(a product equal to 15) 1
21. P(a sum greater than 6) 7
18
12
22. P(a product less than or equal to 2) 1
9
23. P(a sum equal to 12) 1
36
24. Open-Ended Is it possible for an event to have a probability of 1? Explain
your answer. Yes; Answers may vary. Sample: The probability of rolling
a number cube and rolling a number between 1 and 6, inclusive, is 1.
25. Error Analysis Out of 20 coin flips, your classmate gets heads 14 times.
She determines that the experimental probability of getting heads is 12 .
What error did your classmate make? What is the correct value for
experimental probability? Explain. Your classmate confused theoretical
probability with experimental probability. The experimental probability of
getting heads is the number of number of heads divided by the total number
7.
of flips, or 14
= 10
20
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D
Name Class Date Practice
Form K
Experimental and Theoretical Probability
You roll a standard number cube 8 times. The results are shown below.
5, 1, 2, 4, 6, 3, 5, 5
Find the experimental probability of each outcome.
1. P(rolling a 5)
Number of 5s rolled:
Total number of rolls:
3
8
Number of 5s
Experimental probability: Number
of rolls =
3
8
2. P(rolling a 6)
Number of 6s
Experimental probability: Number
of rolls =
1
8
3. P(rolling an even number) 3
8
4. What is the experimental probability of rolling a multiple of 3 on a standard
number cube? For 60 rolls of the number cube, predict the number of rolls
that will result in a multiple of 3. 0.25; 15
Find the theoretical probability of each outcome.
1
1
5. P(rolling a 5) 6
6. P(rolling a 6) 6
1
7. P(rolling an even number) 2
1
8. P(rolling a multiple of 3) 3
A bag contains 1 red marble, 3 green marbles, 1 blue marble, and 1 yellow
marble. Suppose one marble is picked at random. Find the each probability.
1
1
9. P(blue) 6
10. P(not green) 2
5
11. P(not red) 6
5
12. P(not yellow) 6
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Name Class Date Practice (continued)
Form K
Experimental and Theoretical Probability
13. A spinner has 4 equal sections. After 12 spins, the spinner landed on
section A 4 times, section B 5 times, section C 2 times, and section D
1 time.
a. What is the experimental probability of the spinner stopping
A
B
C
D
on section A? 1
3
b. What is the theoretical probability of the spinner stopping
on section A? 14
14. Reasoning If the probability of an event occurring is 1
4 , what is the
3
probability of its complement? 4
Two standard number cubes are rolled. Find each probability.
15. P(a sum equal to 3) 1
18
16. P(a sum not equal to 3) 17 17. P(a sum equal to 12) 1
18
18. Writing An event has a probability of 1. What does this tell you about the
event? Explain. Answers may vary. An event with a probability of 1 is certain
to happen.
19. Error Analysis You and a friend flip a coin 10 times. The coin lands on heads
7 times. Your friend says that the theoretical probability of getting heads is
7
10 . What error did your friend make? What is the correct value for theoretical
probability? Explain. Your friend confused theoretical probability with
because the
experimental probability. The correct theoretical probability is 1
2
coin is equally likely to land on heads or tails.
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36