We can use random numbers to simulate compound events as well as simple events.
Example :
Suppose that there is a 20% chance that a particular volcano will erupt in any given decade. Find an experimental probability that the volcano will erupt in at least 1 of the next 5 decades.
Answer :
Step 1 :
Choose a model.
The probability of an eruption is 20% = 1/5.
Use whole numbers from 1 to 5.
Let 1 represent a decade with an eruption.
Let 2, 3, 4, and 5 represent a decade without an eruption.
Step 2 :
Generate 5 random numbers from 1 to 5. Record the number of decades with an eruption.
5 numbers generated : 3, 1, 3, 4, 2
Eruption decades : 1
Step 3 :
Perform multiple trials by repeating Step 2. Calculate the percent of trials in which there was an eruption in at least 1 of the 5 decades.
Trials
1
2
3
4
5
6
7
8
9
10
Numbers Generated
3, 1, 3, 4, 2
3, 2, 2, 4, 5
1, 3, 3, 2, 5
5, 3, 4, 5, 4
5, 5, 3, 2, 4
2, 3, 3, 4, 2
1, 2, 4, 1, 4
1, 3, 2, 1, 5
1, 2, 4, 2, 5
5, 5, 3, 2, 4
Eruption dec.
1
0
1
0
0
0
2
2
1
0
Step 4 :
In 5 out of the 10 trials, there was an eruption in at least 1 of the 5 decades. The experimental probability of an eruption in at least 1 of the next 5 decades is 5/10 or 50%.
Matt guesses the answers on a quiz with 5 true-false questions. The probability of guessing a correct answer on each question is 50%. Use a simulation to find an experimental probability that he gets at least 2 questions right. (Hint: Use 0s and 1s. Let 0s represent incorrect answers, and 1s represent correct answers. Perform 10 trials, generating 5 random numbers in each, and count the number of 1s.)
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