**Using technology to conduct a simulation :**

We can use the technologies like graphing calculator or computer to generate random numbers and conduct a simulation.

**Example 1 :**

A cereal company is having a contest. There are codes for winning prizes in 30% of its cereal boxes. Find an experimental probability that you have to buy exactly 3 boxes of cereal before you find a winning code.

**Solution :**

**Step 1 : **

Choose a model.

The probability of finding a winning code is 30% = 3/10

Use whole numbers from 1 to 10.

Let three numbers represent buying a box with a winning code.

Winning code: 1, 2, 3

Non winning code: 4, 5, 6, 7, 8, 9, 10

**Step 2 : **

Generate random numbers from 1 to 10 until you get one that represents a box with a winning code. Record how many boxes you bought before finding a winning code.

5 numbers generated: 9, 6, 7, 8, 1

(1 represents a box with a winning code)

**Step 3 : **

Perform multiple trials by repeating Step 2.

Trials

1

2

3

4

5

6

7

8

9

10

Numbers Generated

9, 6, 7, 8, 1

2

10, 4, 8, 1

4, 10, 7, 1

2

4, 3

3

7, 5, 2

8, 5, 4, 8, 10, 3

9, 1

Boxes bought

5

1

4

4

1

2

1

3

6

2

**Step 4 : **

Find the experimental probability.

In 1 of 10 trials, you bought exactly 3 boxes of cereal before finding a winning code.

The experimental probability is 1/10 , or 10%.

**Example 2 :**

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.

**Solution :**

**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%.

**Question 1 :**

An elephant has a 50% chance of giving birth to a male or a female calf. Use a simulation to find an experimental probability that the elephant gives birth to 3 male calves before having a female calf. (Hint: Use 0s and 1s. Let 0 represent a male calf, and 1 represent a female calf. Generate random numbers until you get a 1.)

**Question 2 : **

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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