Dependent Events

Definition

Dependent events are events where the occurrence of one event affects the probability of another event happening. The probability of one event depends on the outcome of another event.

5 Must Know Facts For Your Next Test

1. Dependent events are events where the occurrence of one event affects the probability of another event happening.
2. The probability of one dependent event depends on the outcome of another event that has already occurred.
3. Dependent events are often represented using conditional probability, where the probability of one event is calculated given that another event has already occurred.
4. The multiplication principle is used to calculate the probability of two or more dependent events occurring together, by multiplying their individual probabilities.
5. Understanding the concept of dependent events is crucial for solving probability problems involving the intersection of events or the probability of a sequence of events occurring.

Review Questions

• Explain the difference between dependent and independent events, and provide an example of each.
  • Dependent events are events where the occurrence of one event affects the probability of another event happening. For example, the probability of drawing a red card from a deck of cards depends on whether a black card was drawn previously. Independent events, on the other hand, are events where the occurrence of one event does not affect the probability of another event. For example, the probability of flipping a coin and getting heads does not depend on the outcome of a previous coin flip.
• Describe how the multiplication principle is used to calculate the probability of two or more dependent events occurring together.
  • The multiplication principle states that the probability of two or more dependent events occurring together is equal to the product of their individual probabilities. For example, if the probability of event A occurring is 0.6 and the probability of event B occurring, given that event A has already occurred, is 0.4, then the probability of both events A and B occurring together is 0.6 × 0.4 = 0.24.
• Analyze how the concept of dependent events is applied in the context of 3.3 Two Basic Rules of Probability and 3.6 Probability Topics.
  • The concept of dependent events is crucial in understanding the two basic rules of probability: the addition rule and the multiplication rule. The addition rule is used to calculate the probability of the union of two or more mutually exclusive events, while the multiplication rule is used to calculate the probability of the intersection of two or more dependent events. Additionally, in the context of 3.6 Probability Topics, the concept of dependent events is essential for understanding conditional probability and the use of the multiplication principle to solve complex probability problems involving sequences of events or the intersection of events.

Related terms

Independent Events: Independent events are events where the occurrence of one event does not affect the probability of another event happening. The probability of one event is not influenced by the outcome of another event.

Conditional Probability: Conditional probability is the likelihood of an event occurring given that another event has already occurred. It is the probability of one event happening, given that another event has already happened.

Multiplication Principle: The multiplication principle states that the probability of two or more dependent events occurring together is equal to the product of their individual probabilities.