13B.2 - Tables and Grids

Tables and grids

Tables and grids (also known as arrays) can be used to show the outcomes in a sample space with only two events. If you need to represent more than two events you need to use a tree diagram. The benefit of a table over a tree diagram is the ability to represent two events which have many outcomes that would be tedious to represent using branches.

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Rolling two dice

The following table show the sample space for rolling two dice:

Table 1 - The sample space when two dice are rolled.

Consider:

• What is the probability of rolling at least one 6?
• What is the probability that both numbers are even?
• What is the probability of rolling a double?

While the table above represents the two faces shown on the dice, we might be interested in a particular operation of those two numbers.

The sum of the two numbers

Consider the addition of the two numbers on the dice, the table below shows represents the sample space for this random experiment.

Table 2 - The sample space for the sum of two dice.

From the table above you can clearly see that the probabilities for the events in this sample space are not equal. The probability of 'getting a 7' is much greater than 'getting a 3'.

The product of the two numbers

Consider the multiplication of the two numbers on the dice, the table below shows represents the sample space for this random experiment.

Table 3 - The sample space for the product of two dice.

From the table above you can clearly see that the probabilities for the events in this sample space are not equal. The probability of 'getting a 12' is much greater than 'getting a 36'.

13B.2 - Exercises:

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