Real-World Examples of the Complement Rule in Action

📚 Quick Study Guide

• 🔢 The complement rule states that the probability of an event not happening is 1 minus the probability of the event happening.
• 📝 Formula: $P(A') = 1 - P(A)$, where $P(A')$ is the probability of event A not happening, and $P(A)$ is the probability of event A happening.
• 🎲 The complement rule is useful when calculating the probability of an event happening is more complex than calculating the probability of it not happening.
• 💡 It simplifies calculations in scenarios like 'at least one' problems.

Practice Quiz

1. What does the complement rule help you find?
   1. The probability of an event occurring.
   2. The probability of an event not occurring.
   3. The sum of all probabilities.
   4. The average of all probabilities.
2. If the probability of rain is 30%, what is the probability that it will not rain, according to the complement rule?
   1. 30%
   2. 60%
   3. 70%
   4. 100%
3. In a class of 25 students, 10 are girls. If a student is chosen at random, what is the probability that the student is not a girl?
   1. 10/25
   2. 15/25
   3. 5/25
   4. 20/25
4. If you roll a fair six-sided die, what is the probability that you will not roll a 4?
   1. 1/6
   2. 2/6
   3. 5/6
   4. 4/6
5. A bag contains 5 red balls and 3 blue balls. If you pick a ball at random, what is the probability that it is not blue?
   1. 3/8
   2. 5/8
   3. 2/8
   4. 1/8
6. What is the probability of *not* drawing an Ace from a standard deck of 52 cards?
   1. 4/52
   2. 1/52
   3. 48/52
   4. 51/52
7. In a survey, 65% of people prefer coffee. What percentage of people do not prefer coffee?
   1. 65%
   2. 35%
   3. 45%
   4. 55%