# DESIGNING AND CONDUCTING A SIMULATION FOR A COMPOUND EVENT

## About "Designing and conducting a simulation for a compound event"

Designing and conducting a simulation for a compound event :

We can use random numbers to simulate compound events as well as simple events.

## Designing and conducting a simulation for a compound event - Example

Question :

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.

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

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%.

## Practice question

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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