The relationship between multiple events that occur is important. The key question that you need to think about is, “does the first event influence the outcome of the next event?”

For example, consider a pair of number cubes. One cube is red and the other cube is white. Let’s assume that both number cubes are fair cubes; that is, each number on each cube has an equal chance of landing on the top face.

If you roll both cubes, does the number that appears on the top face of the red number cube affect the number that appears on the top face of the white number cube? Why do you think that is the case?

Check Your Answer

No. The number cubes may bounce off one another, but the number appearing on the top face of the white number cube does not depend on the number that appears on the top face of the red number cube.

Sort the following situations into two categories: situations where the outcome of the second event depends on the outcome of the first event, and situations where the outcome of the second event does not depend on the outcome of the first event.

Drag the tile containing the descriptors into the appropriate column.

When you have a series of compound events where the outcome of the first event affects the outcomes of the subsequent events, these events are called dependent events. We can say that the outcome of the second event depends on the outcome of the first event.

When you have a series of compound events where the outcome of the first event does not affect the outcomes of the subsequent events, these events are called independent events. We can say that the outcome of the second event is independent of the outcome of the first event.

Practice

Determine whether the following events are independent events or dependent events.

1. Tina flips a coin and rolls a number cube.

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   Will the number that appears on the top face of the number cube depend on whether or not the coin lands with heads facing up?
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   Check Your Answer

   Independent events
2. Herb reaches into a box containing 12 instant oatmeal packages and randomly selects one package of cinnamon oatmeal and one package of maple oatmeal.

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   After Herb selects the first package, are there still 12 packages to choose from when selecting the second package?

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   Check Your Answer

   Dependent events

3. Shirley reaches into a box containing 12 instant oatmeal packages and randomly selects one package of blueberry oatmeal. She replaces the package, and then randomly selects another package of blueberry oatmeal.

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   Does Shirley have the same number of packages from which to select for the second draw as the first draw?

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   Check Your Answer

   Independent events

4. Mrs. Siddiqi is an inspector on a computer assembly line. Of the 20 computers on the assembly line, she randomly selects 3 computers for detailed inspection.

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   After Mrs. Siddiqi selects the first computer, are there still 20 computers on the assembly line?

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   Check Your Answer

   Dependent events