**Using experimental probability to make predictions :**

In this section, we are going to see, how experimental probability can be used to make predictions.

**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

Hence, 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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