Activity 4.1.1 Data Exploration
Introduction
The understanding and manipulation of data allows decision making to be based on
outcomes and even predictions. Statistical calculations can be theory-based.
Calculations can also be established through manipulation of data collection or
experimentation. To better understand the advantages and limitations of both
processes of probability, statisticians must have understanding and experience
working with both theory and experimental data.
Equipment



Coin
Dice or digital dice
Calculator
Procedure
1. What is the probability that the illustrated board game spinner will land on blue?
a. Define the Experiment
b. Define the Sample Space
c. Define the Event
d. Solve for Probability
2. What is the probability of a flipped coin landing on heads?
3. What is the probability of a flipped coin landing on heads 4 times out of 6 trials?
4. Calculate the probability of a flipped coin landing on heads through
experimentation.
a. Toss a fair coin 10 times and record your data below.
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Principles of Engineering Activity 4.1.1 Data Exploration – Page 1
Toss
1
2
3
4
5
6
7
8
9
10
Total
Heads
Tails
b. Calculate the relative frequency of the coin landing on heads after 10
trials.
c. Toss a fair coin 50 times and record your data below.
Toss
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Heads
Tails
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Principles of Engineering Activity 4.1.1 Data Exploration – Page 2
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Total
d. Calculate the relative frequency of the coin landing on heads after 50
trials.
e. Collect the relative frequency data from your entire class and determine
the relative frequency of the coin landing on heads.
f. Describe the relationship between the relative frequency of the coin
landing on heads and the probability of a single coin landing on heads.
Does sample size affect this relationship?
5. Create a histogram representing the summation possibilities of rolling two dice
simultaneously (Note: rolling a 2 and a 3 is not the same as rolling a 3 and a 2).
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Principles of Engineering Activity 4.1.1 Data Exploration – Page 3
Sum
Event
Frequency
6. What is the probability of rolling a 7?
7. What is the probability of rolling a 12?
8. What is the probability of not rolling a 9?
9.
Trial
Simultaneously roll two dice 50 times and record your data below.
1
2
3
Die #1
4
5
6
1
2
3
Die #2
4
5
6
Total
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Principles of Engineering Activity 4.1.1 Data Exploration – Page 4
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
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Principles of Engineering Activity 4.1.1 Data Exploration – Page 5
48
49
50
Total
a. What is the relative frequency of rolling a summation of 7?
b. What is the relative frequency of rolling a summation of 12?
c. What is the relative frequency of rolling a 6 on a single die?
d. What is the relative frequency of rolling a summation of 6?
e. Were your dice loaded? Justify your answer.
Conclusion
10. One coin is flipped four times. What is the probability of flipping two heads and
two tails?
11. A set of two die are rolled twice. What is the probability of rolling “snake eyes” on
both rolls?
12. A sunglasses manufacturer receives frames from three manufacturing
companies. What is the probability that a defective frame was manufactured by
company three?
Factory
1
2
3
Percent of Production
62%
30%
8%
Probability of Defect
.020
.013
.027
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Principles of Engineering Activity 4.1.1 Data Exploration – Page 6