CALCULATING THEORETICAL PROBABILITY OF SIMPLE EVENTS

Theoretical probability is the probability that an event occurs when all of the outcomes of the experiment are equally likely.

The formula given below can be used to find theoretical probability.

Probability can be written as a fraction, a decimal, or a percent.

For example, the probability of a particular event is 5/16. We can also write that as 0.3125 or as 31.25%.

Examples

Example 1 :

A bag contains 6 red marbles and 12 blue ones. You select one marble at random from the bag. What is the probability that you select a red marble ? Write your answer in simplest form.

Solution :

Step 1 :

Find the number of ways the event can occur, that is, the number of red marbles : 6.

Step 2 :

Find the total number of equally likely outcomes by adding number of red marbles and number of blue marbles. 

6 + 12  =  18

There are 18 possible outcomes in the sample space.

Step 3 : 

Find the probability of selecting a red marble.

P  =  No. of red marbles / Total no. of marbles

P  =  6/18

The probability that you select a red marble is 6/18 , or 1/3 .

Example 2 :

At a school fair, we have a choice of spinning Spinner A or Spinner B. We win an MP3 player if the spinner lands on a section with a star in it. Which spinner should we choose if we want a better chance of winning ?

Solution :

Let us find probabilities of getting a star in both spinner A and spinner B.

Compare the probabilities and choose which spinner has better chance of winning. 

Spinner A :

Total number of sections  =  8

Number of sections with stars  =  3

The formula given below can be used to find probability.

Probability (A)  =  3/8  =  0.375 or 37.5 % 

Spinner B :

Total number of sections  =  16

Number of sections with stars  =  5

Probability (B)  =  5/16  =  0.3125 or 31.25 % 

Conclusion : 

The probability of getting a star in Spinner A is greater than  Spinner B.  So, we should choose for a better chance of winning

Reflect

Theoretical probability is a way to describe how we found the chance of winning an MP3 player in the scenario above. Using the spinner example to help you, explain in your own words how to find the theoretical probability of an event.

The theoretical probability of an event is a ratio comparing the number of ways the event can occur to the total number of outcomes for the experiment.

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