The Complement of an Event A | Summary and Q&A

TL;DR

The complement of an event is the opposite of that event, and the probability of an event and its complement adds up to 1.

Key Insights

• ❓ The complement of an event represents the opposite of that event.
• 🪜 The probability of an event and its complement always adds up to 1.
• ❓ Probability calculations often involve converting percentages into decimals.
• ➖ The formula 1 minus the probability of the complement can be used to calculate the probability of an event.
• 💨 Complement events provide a simple way to solve probability problems.
• 🔙 The notation for the complement of an event can be represented as A' or AC.
• ❓ Probability calculations require understanding the concept of complements.

Transcript

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Questions & Answers

Q: How do you write the complement of an event?

The complement of an event A is written as A' or AC. It represents the event that A does not occur.

Q: What is the probability of an event and its complement adding up to?

The probability of an event A plus the probability of its complement equals 1. This is because an event can either happen or not happen, covering all possibilities.

Q: How can the probability of an event be calculated using the complement?

By using the formula, the probability of an event A can be calculated as 1 minus the probability of its complement. This formula allows for the calculation of probabilities based on complement events.

Q: How can percentages be converted into decimals for probability calculations?

To convert percentages into decimals for probability calculations, move the decimal point two places to the left. For example, 0.62% becomes 0.0062.

Summary & Key Takeaways

• The complement of an event A is the event that A does not occur.

• The probability of an event A plus the probability of its complement equals 1.

• Using the formula, the probability of an event A can be calculated by subtracting the probability of its complement from 1.