**Designing and conducting a simulation for a compound event :**

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

**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.

**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.)

After having gone through the stuff given above, we hope that the students would have understood "How to design and conduct a simulation for a compound event".

Apart from the stuff given above, if you want to know more about "Designing and conducting a simulation for a compound event", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**