# 3. Calculating Probabilities of Multiple Events

Overview

We often want to know if one event and another event will occur, or if one event or another event will occur. Learn how to calculate probabilities like this in this lesson.

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Summary

1. Lesson Goal (00:11)

The goal of this lesson is to calculate the probabilities of multiple events occurring.

2. Probability for an AND Event (00:31)

An AND event occurs when we want to find the probability of one event and another event occurring. If we can visualize every combination of outcomes for the two events, then we can calculate this probability by dividing the number of outcomes where the event occurs by the total number of possible outcomes.

Alternatively, we can calculate the probability of both events by multiplying the probability of the first event by the probability of the second event. However, this only applies if the events are independent events, that is the outcome of one event does not affect the outcome of the other event.

3. An OR Event with No Overlap (02:42)

An OR event occurs when we want to find the probability of one event or another event occurring. How we calculate this probability depends on whether there is any overlap between the events, that is if there are any outcomes where both events occur at the same time.

If the two events have no overlap, we can find the probability of one event or the other occurring by adding the probabilities for the individual events. In this situation, the events are described as mutually exclusive, as the events cannot occur together.

4. An OR Event with Overlap (04:18)

If two events are not mutually exclusive, then there are some outcomes where both events occur at the same time. In this case, adding the probabilities of the individual events would double count these overlapping outcomes. As a result, to calculate the probability of one event or another event occurring, we should add the probabilities of the individual events, then subtract the probability of both events occurring.

Transcript

Applications of Probability
Probability Principles

Contents

09:00

04:55

06:12

05:35

07:25

06:50

06:03

04:20

#### 9. Understanding Sampling

06:39

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