# Probability of Complementary Events & Sample Space | Summary and Q&A

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March 23, 2019
by
The Organic Chemistry Tutor
Probability of Complementary Events & Sample Space

## TL;DR

This analysis explores the probability of events and their complements, using examples of rolling a die and selecting marbles from a bag.

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### Q: How can we calculate the probability of event A and event B occurring together?

To calculate this, we find the intersection of event A and event B, which consists of the numbers 3 and 4. The probability is then 2/6 or 1/3.

### Q: What is the probability of event A or event B occurring?

By finding the union of event A and event B, we get all numbers except 6. This results in 5 favorable outcomes out of 6, giving a probability of 5/6 or approximately 83.3%.

### Q: What is the probability of the complement of event A occurring?

The complement of event A includes the numbers 5 and 6. With 2 favorable outcomes out of 6, the probability is 2/6 or 1/3.

### Q: How does the probability of event A and its complement relate?

The sum of the probability of event A occurring and the probability of its complement occurring adds up to 1. This relationship is summarized as P(A) + P(A̅) = 1.

## Summary & Key Takeaways

• Sample space for rolling a 6-sided die includes outcomes ranging from 1 to 6.

• Event A includes outcomes less than or equal to 4, while event B includes outcomes 3, 4, and 5.

• The probability of both event A and event B occurring is 1/3, and the probability of event A or event B occurring is approximately 83.3%.