Pre-Calculus probability quiz: General Addition Rule

📚 Quick Study Guide

• 🧮 The General Addition Rule is used to find the probability of either of two events occurring.
• ➕ The formula is: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, where:
  • $P(A \cup B)$ is the probability of either A or B occurring.
  • $P(A)$ is the probability of A occurring.
  • $P(B)$ is the probability of B occurring.
  • $P(A \cap B)$ is the probability of both A and B occurring.
• 🤝 If A and B are mutually exclusive events (they cannot both occur), then $P(A \cap B) = 0$, and the formula simplifies to $P(A \cup B) = P(A) + P(B)$.
• 💡 Remember to subtract the intersection to avoid double-counting outcomes that are in both events.

📝 Practice Quiz

1. What does $P(A \cup B)$ represent in the General Addition Rule?
   1. The probability of A occurring.
   2. The probability of B occurring.
   3. The probability of both A and B occurring.
   4. The probability of either A or B occurring.
2. What is the formula for the General Addition Rule?
   1. $P(A \cup B) = P(A) + P(B) + P(A \cap B)$
   2. $P(A \cup B) = P(A) - P(B) - P(A \cap B)$
   3. $P(A \cup B) = P(A) + P(B) - P(A \cap B)$
   4. $P(A \cup B) = P(A) - P(B) + P(A \cap B)$
3. If events A and B are mutually exclusive, what is $P(A \cap B)$?
   1. 1
   2. 0.5
   3. 0
   4. It depends on P(A) and P(B)
4. A card is drawn from a standard deck. Let A be the event that the card is a heart, and B be the event that the card is a king. What is $P(A \cup B)$?
   1. 4/13
   2. 1/2
   3. 1/4
   4. 1/13
5. In a class, 60% of the students like math, and 70% like science. 40% like both. What percentage of students like either math or science?
   1. 90%
   2. 50%
   3. 30%
   4. 20%
6. A die is rolled. Let A be the event that the number is even, and B be the event that the number is less than 4. What is $P(A \cup B)$?
   1. 5/6
   2. 1/2
   3. 2/3
   4. 1/3
7. A bag contains 3 red balls and 5 blue balls. Two balls are drawn without replacement. Let A be the event that the first ball is red, and B be the event that the second ball is blue. What is P(A)?
   1. 3/8
   2. 5/8
   3. 3/7
   4. 5/7