Laura Buckles
Activity 4.1 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
Spinning the game spinner
b. Define the Sample Space
Blue, magenta, yellow, purple, green, pink
c. Define the Event
Spinner landing on blue
d. Solve for Probability
1/6 or 16.66%
2. What is the probability of a flipped coin landing on heads?
50%
3. What is the probability of a flipped coin landing on heads 4 times out of 6 trials?
23.44%
© 2012 Project Lead The Way, Inc.
POE Activity 4.1 Data Exploration – Page 1
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.
Toss
1
2
3
4
5
6
7
8
9
10
Total
Heads
Tails
X
X
x
x
X
x
x
x
x
x
4
6
b. Calculate the relative frequency of the coin landing on heads after 10
trials.
40%
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
Heads
Tails
X
X
X
X
x
x
X
x
x
x
x
X
X
X
X
X
X
X
X
x
X
X
X
X
© 2012 Project Lead The Way, Inc.
POE Activity 4.1 Data Exploration – Page 2
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Total
X
X
x
X
X
X
X
x
X
X
X
X
X
x
X
X
X
X
X
X
X
X
X
X
X
x
25
25
d. Calculate the relative frequency of the coin landing on heads after 50
trials.
50%
e. Collect the relative frequency data from your entire class and determine
the relative frequency of the coin landing on heads.
244 heads 256 tails
48.8% heads
51.2% tails
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?
The percents are very close to the theoretical probability. They are a little off
but results usually vary by each test.
The greater the sample size, the closer the percents will be to the
theoretical ones.
© 2012 Project Lead The Way, Inc.
POE Activity 4.1 Data Exploration – Page 3
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).
Sum
2
1,1
Event
Frequency
1
3
1,2 ;2,1
2
4
1,3; 2,2; 3,1
3
5
1,4; 2,3; 3,2; 4,1
4
6
1,5; 2,4; 3,3; 4,2; 5,1
5
7
1,6; 2,5; 3,4; 4,3; 5,2; 6,1
6
8
2,6; 3,5; 4,4; 5,3; 6,2
5
9
3,6; 4,5; 5,4; 6,3
4
10
4,6 ;5,5 ;6,4
3
11
5,6; 6,5
2
12
6,6
1
6. What is the probability of rolling a 7?
1/6
7. What is the probability of rolling a 12?
© 2012 Project Lead The Way, Inc.
POE Activity 4.1 Data Exploration – Page 4
1/36
8. What is the probability of not rolling a 9?
8/9
9.
red
Trial
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
Simultaneously roll two dice 50 times and record your data below.
1
2
Die #1
3
4
5
x
6
x
1
x
x
2
Die #2
3
4
x
5
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
6
x
x
x
x
green
Total
6
3
9
6
7
8
10
7
7
6
7
6
10
7
6
4
3
3
7
10
8
6
11
6
6
8
6
5
7
7
8
10
8
11
7
6
8
8
3
5
© 2012 Project Lead The Way, Inc.
POE Activity 4.1 Data Exploration – Page 5
41
42
43
44
45
46
47
48
49
50
Total
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
9
7
4
9
6
3
6
3
4
8
9
14
Sums
5
x
9
4
9
x
9
6
7
14
x
9
5
3: 6 times
4: 3 times
5: 2 times
6: 12 times
7:10 times
8: 8 times
9: 3 times
10: 4 times
11: 2 times
a. What is the relative frequency of rolling a summation of 7?
20% 10/50
b. What is the relative frequency of rolling a summation of 12?
0%
c. What is the relative frequency of rolling a 6 on a single die?
1/6
d. What is the relative frequency of rolling a summation of 6?
12/50 24%
e. Were your dice loaded? Justify your answer.
No, the results will vary on how the dice are rolled and the surface they’re rolled on.
Also on the number of rolls.
Conclusion
10. One coin is flipped four times. What is the probability of flipping two heads and
two tails?
© 2012 Project Lead The Way, Inc.
POE Activity 4.1 Data Exploration – Page 6
6/16 37.5%
11. A set of two die are rolled twice. What is the probability of rolling “snake eyes” on
both rolls?
2/72 or 2.77%
12. A sunglasses manufacturer receives frames from three manufacturing
companies. What is the probability that a defective frame was manufactured by
company three?
21.6%
Factory
1
2
3
Percent of Production
62%
30%
8%
Probability of Defect
.020
.013
.027
© 2012 Project Lead The Way, Inc.
POE Activity 4.1 Data Exploration – Page 7