USING A SIMULATION TO MAKE A PREDICTION

We can use a simulation or model of an experiment to find the experimental probability of compound events.

Example 1 : 

At a street intersection, a vehicle is classified either as a car or a truck, and it can turn left, right, or go straight. About an equal number of cars and trucks go through the intersection and turn in each direction. Use a simulation to find the experimental probability that the next vehicle will be a car that turns right.

Solution : 

Step 1 :

Choose a model.

Use a coin toss to model the two vehicle types.

Let Heads  =  Car and Tails  =  Truck

Use a spinner divided into 3 equal sectors to represent the three directions as shown.

Step 2 : 

Find the sample space for the compound event.

There are 6 possible outcomes: CL, CR, CS, TL, TR, TS

Step 3 : 

Perform the simulation.

A coin was tossed and a spinner spun 50 times.

The results are shown in the table.

Step 3 : 

Find the experimental probability that a car turns right.

Substitute the values. 

P (Car turns right)  =  6/50

Simplify.

P (Car turns right)  =  3/25.

Based on the simulation, the experimental probability is 3/25 that the next vehicle will be a car that turns right.

Example 2 : 

A jeweler sells necklaces made in three sizes and two different metals. Use the data from a simulation to find the experimental probability that the next necklace sold is a 20-inch gold necklace.

Solution : 

Step 1 : 

Find the total no. of necklaces made.  

Total no. of necklaces is 

=  12 + 16 + 5 + 22 + 8 + 12 

=  75

Step 2 : 

Find the no. of 20-inch gold necklaces.

No. of 20-inch gold necklaces  =  12.

Step 3 : 

Find the probability. 

Experimental probability  =  12/75

Simplify.

Experimental probability  =  4/25

Example 3 : 

A dentist has 400 male and female patients that range in ages from 10 years old to 50 years old. Use the data from a simulation to find the experimental probability that the next patient will be female and in the age range 22–39.

Solution : 

Step 1 : 

Find the total no. of patients. 

Total no. of patients is 

=  44 + 66 + 32 + 53 + 36 + 50 + 45 + 74

=  400

Step 2 : 

Find the no. of female patients in the age range 22 - 39.

No. of female patients in the age range 22 - 39  =  50

Step 3 : 

Find the probability. 

Experimental probability  =  50/400

Simplify.

Experimental probability  =  1/8

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