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Testing the Probability of Six in a Simulated Die Toss

Testing the probability of rolling a six in a simulated die toss is similar to testing the probability of the point landing up when tossing a thumbtack. You will need to make a table like the following for your results. The die was tossed 60 times for this example. To save space, the results for the first 30 tosses are shown on the left side of the table and the results for the last 30 tosses are shown on the right sided of the table. Since you must toss the tack 100 times, your table will be somewhat longer. The percent of sixes is found by dividing the total sixes by the toss number and multiplying the result by 100%.

Toss #
Result
Six?
Total Sixes
% Sixes
 
Toss #
Result
Six?
Total Sixes
% Sixes
1
4
No
0
0.0
31
5
No
2
6.5
2
1
No
0
0.0
32
1
No
2
6.3
3
2
No
0
0.0
33
4
No
2
6.1
4
4
No
0
0.0
34
5
No
2
5.9
5
5
No
0
0.0
35
5
No
2
5.7
6
6
Yes
1
16.7
36
4
No
2
5.6
7
1
No
1
14.3
37
4
No
2
5.4
8
4
No
1
12.5
38
3
No
2
5.3
9
6
Yes
2
22.2
39
1
No
2
5.1
10
4
No
2
20.0
40
1
No
2
5.0
11
1
No
2
18.2
41
6
Yes
3
7.3
12
2
No
2
16.7
42
1
No
3
7.1
13
1
No
2
15.4
43
6
Yes
4
9.3
14
1
No
2
14.3
44
5
No
4
9.1
15
5
No
2
13.3
45
4
No
4
8.9
16
5
No
2
12.5
46
5
No
4
8.7
17
1
No
2
11.8
47
5
No
4
8.5
18
5
No
2
11.1
48
2
No
4
8.3
19
3
No
2
10.5
49
1
No
4
8.2
20
3
No
2
10.0
50
6
Yes
5
10.0
21
2
No
2
9.5
51
1
No
5
9.8
22
5
No
2
9.1
52
3
No
5
9.6
23
2
No
2
8.7
53
4
No
5
9.4
24
3
No
2
8.3
54
5
No
5
9.3
25
5
No
2
8.0
55
6
Yes
6
10.9
26
3
No
2
7.7
56
4
No
6
10.7
27
3
No
2
7.4
57
1
No
6
10.5
28
1
No
2
7.1
58
5
No
6
10.3
29
4
No
2
6.9
59
4
No
6
10.2
30
2
No
2
6.7
60
2
No
6
10.0

 

From this test, the empirical probability of rolling a six is 10.0%. The graph of the percent of sixes versus the toss number is shown below. For 100 tosses, you may want to rotate your graph ninety degrees clockwise so that the toss number axis takes up the longer dimension of the page.

 

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