CALCULATING EXPERIMENTAL PROBABILITY OF COMPOUND EVENTS

The experimental probability of a compound event can be found using recorded data.

Let us look at some examples to understand how experimental probability of a compound event can be calculated. 

Example 1 : 

A food trailer serves chicken and records the order size and sides on their orders, as shown in the table. What is the experimental probability that the next order is for 3-pieces with cole slaw ?

Solution :

Step 1 : 

Find the total number of trials, or orders.

33 + 22 + 52 + 35 + 13 + 55 + 65 + 55  =  330

Step 2 :

Find the number of orders that are for 3 pieces with cole slaw : 55.

Step 3 :

Find the experimental probability.

P(3 piece + slaw) :

=  (number of 3 piece + slaw) / Total number of orders

Substitute the values

=  55/330

Simplify

=  1/6

So, the experimental probability that the next order is for 3 pieces of chicken with cole slaw is 1/6. 

Example 2 : 

Drink sales for an afternoon at the school carnival were recorded in the table. What is the experimental  probability that the next drink is a small cocoa ? 

Solution :

Step 1 : 

Find the total number of trials, or drink sales.

77 + 98 + 60 + 68 + 45 + 52  =  400

Step 2 :

Find the number of drink sales that are small coca. 

Step 3 :

Find the experimental probability.

P(small cocoa) :

=  (number of small cocoa) / Total number of drink sales

Substitute the values

=  60/400

Simplify

=  3/20

So, the experimental probability that next drink is a small cocoa is 3/20. 

Example 3 : 

A dentist has 400 male and female patients that range in ages from 10 years old to 50 years old and up as shown in the table. What is 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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