USING EXPERIMENTAL PROBABILITY TO MAKE PREDICTIONS

The following steps will be useful to make predictions using experimental probability. 

Step 1 : 

Using the given data, find experimental probability of an event. 

Step 2 :

Make predictions by multiplying experimental probability and total number of trials. 

Example 1 : 

The table shows the number of necklaces sold in three sizes and two different metals by a jeweler in January 2017. If had sold 100 necklaces in February 2017, about how many 20-inch gold necklaces would he have sold ? 

Solution : 

Step 1 : 

Since we want to make predictions for 20-inch gold necklaces, first we have to find experimental probability for 20-inch gold necklaces from the given data. 

Find experimental probability for 20-inch gold necklaces. 

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

Step 4 : 

Now make prediction for 20-inch gold necklaces in the total of 100 necklaces sold in Feb 2017.   

Multiply the experimental probability and the total number of necklaces sold in Feb. 

=  (4/25) x 100

Simplify.

=  4 x 4

=  16

So, he would have sold sixteen 20-inch gold necklaces in Feb 2017. 

Example 2 : 

The table given below shows the number of male and female patients that range in ages from 10 years old to 50 years old having had by a dentist in the year 2015. If the dentist had 600 patients in the year 2016, about how many female patients in the age range 22–39 can be expected ?

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

Step 4 : 

Now make prediction for female patients in the age range 22–39.   

Multiply the experimental probability and the total number of patients in the year 2016. 

=  (1/8) x 600

=  600/8

Simplify

=  75

In the year, 75 female patients in the age range 22–39 can be expected.  

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