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Statistics
THEORETICAL PROBABILITY
Example 1: Determine the Theoretical Probability:
Mr. Ram and his bro are playing Predicting Products. They take turns to roll 2 dice, each labelled 1 to 6. If the product of the 2 numbers rolled is odd, Mr. Ram gets a point. If the product is even, his bro gets a point. The first person to get 20 points wins.
Who is more likely to win?
Here is one way to predict the winner using theoretical probability:
Organize the possible outcomes in a table. Each number on a die has an equal chance of being rolled.
We say: the probability of getting an even product is 27 out of 36.
We write the probability of an even product as a fraction: 27/36
We say: the probability of getting an odd product is 9 out of 36.
We write the probability of an odd product as a fraction: 9/36
Each of these probabilities is a theoretical probability.
A theoretical probability is the likelihood that an outcome will happen.
Theoretical Probability =
Number of favorable outcomes
Number of possible outcomes
The probabiltiy that Mr. Ram wins is 9/36
The probability that his bro wins is 27/36
Since 27/36 > 9/36, His bro is more likely to win.
Practice
Practice PDFs available for download:
EXPERIMENTAL
PROBABILITY
Example 1: Determine the Experimental Probability
Winnie and Selina put colored cubes into a bag. They used 4 blue, 2 red, 2 green, and 2 yellow cubes. A cube is picked from the bag at random. The theoretical probability that a blue cube is picked is 4/10.
Winnie and Selina planned an experiment for the class.
Each student would pick a cube from the bag without looking, then replace it.
She would do this 10 times.
Here are the results of one experiment.
The blue cube was picked 6 times.
The experimental probability is the likelihood that something occurs based on the results of an experiment.
Experimental Probability =
Number of times an outcome occurs
Number of times the experiment is conducted
So, the experimental probability of picking a blue cube is 6/10 or 3/5.
Here are the results for 100 trials:
The blue cube was picked 43 times. So, the experimental probability of picking a blue cube is 43/100
The experimental probability is close to the theoretical probability of 4/10
The more trial we conduct, the closer the experimental probability may come to the theoretical probability.
Practice
Practice PDFs available for download:
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