Replacement

Definition

Replacement in probability refers to whether an item is put back into the population after being selected. If replacement occurs, the probabilities remain unchanged for subsequent selections.

5 Must Know Facts For Your Next Test

1. With replacement, each selection is independent of previous selections.
2. Without replacement, the total number of items decreases with each selection, affecting probabilities.
3. Replacement ensures that multiple events do not influence each other’s outcomes.
4. In calculating probabilities with replacement, the sample space remains constant.
5. Without replacement is commonly used in scenarios like drawing cards from a deck without putting them back.

Review Questions

• What impact does replacement have on the independence of events?
• How does 'with replacement' affect the sample space in probability calculations?
• Give an example where you would use 'without replacement' in a probability problem.

Related terms

Independent Events:

Events where the outcome of one event does not affect the outcome of another.

Mutually Exclusive Events:

Events that cannot happen at the same time.

Sample Space:

The set of all possible outcomes in a probability experiment.