Part One: Probability
Case Study #1.10: Rare Event Approach
Case
Description: Demonstrate the Rare Event Approach
Experiment I:
We toss a pair
of fair, independently operating 10-sided dice, and observe the sum of the face
values.
The sums and
probabilities are listed below. You can and should verify them later.
Sum Percent
Probability
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2 1.00
3 2.00
4 3.00
5 4.00
6 5.00
7 6.00
8 7.00
9 8.00
10 9.00
11 10.00
12 9.00
13 8.00
14 7.00
15 6.00
16 5.00
17 4.00
18 3.00
19 2.00
20 1.00
Case
Objectives:
According to
the model in experiment I, the event that SUM=2 shows should be a relatively
rare event. Track the occurrence of SUM=2 in 100 tosses of a pair of faair
ten-sided dice (2D10).
According to
the model in experiment I, the event that 10 £ SUM £ 12 should not be a relatively rare event. Track the
occurrence of 10 £ SUM £ 12 in 100 tosses of a pair of fair ten-sided dice (2D10).
Experiment II:
We toss a pair
of fair, independently operating 20-sided dice, and observe the sum of the face
values.
The sums and
probabilities are listed below. You can and should verify them later, if you
have too much free time.
Sum
Number Probability Cumulative Cumulative
of Pairs Percent
Frequency Percent
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2 1 0.25
1 0.25
3 2 0.50 3
0.75
4 3 0.75
6 1.50
5 4 1.00
10 2.50
6 5 1.25
15 3.75
7 6 1.50
21 5.25
8 7 1.75 28 7.00
9 8 2.00
36 9.00
10 9 2.25
45 11.25
11 10 2.50
55 13.75
12 11 2.75
66 16.50
13 12
3.00 78 19.50
14 13 3.25
91 22.75
15 14 3.50
105 26.25
16 15 3.75
120 30.00
17 16 4.00
136 34.00
18 17 4.25
153 38.25
19 18 4.50
171 42.75
20 19 4.75
190 47.50
21 20 5.00
210 52.50
22 19 4.75
229 57.25
23 18 4.50
247 61.75
24 17 4.25
264 66.00
25 16 4.00
280 70.00
26 15 3.75
295 73.75
27 14 3.50 309 77.25
28 13 3.25
322 80.50
29 12 3.00
334 83.50
30 11 2.75
345 86.25
31 10 2.50
355 88.75
32 9 2.25
364 91.00
33 8 2.00
372 93.00
34 7 1.75
379 94.75
35 6 1.50
385 96.25
36 5 1.25
390 97.50
37 4 1.00
394 98.50
38 3 0.75
397 99.25
39 2 0.50
399 99.75
40 1 0.25 400 100.00
Case
Objectives:
According to
the model in experiment II, the event that SUM=2 shows should be a rare event (Pr{SUM=2}=.025). Track the occurrence
of SUM=2 in 100 tosses of a pair of fair twenty-sided dice (2D20).
According to
the model in experiment II, the event that 10 £ SUM £ 20 should not be a relatively rare event (Pr{10 £ SUM £ 20}=.385). Track the occurrence of 10 £ SUM £ 20 in 100 tosses of a pair of fair twenty-sided dice
(2D20).