AP Biology Questions on the Sum Rule

📚 Quick Study Guide

• 🧬 The Sum Rule is used to calculate the probability of either one event OR another event occurring.
• ➕ If events A and B are mutually exclusive (they cannot happen at the same time), the probability of A or B occurring is: $P(A \text{ or } B) = P(A) + P(B)$.
• ✏️ If events A and B are NOT mutually exclusive (they can happen at the same time), the probability of A or B occurring is: $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$.
• 💡 Remember to subtract the probability of both events happening together when they are not mutually exclusive to avoid double-counting.

🧪 Practice Quiz

1. Which of the following scenarios requires the use of the Sum Rule?
   1. A) Determining the probability of rolling a 3 on a six-sided die.
   2. B) Determining the probability of rolling a 3 or a 4 on a six-sided die.
   3. C) Determining the probability of rolling a 3 and then a 4 on a six-sided die.
   4. D) Determining the probability of not rolling a 3 on a six-sided die.
2. In a population of flowers, 30% are red and 20% are white. If a flower is chosen at random, what is the probability that it is either red or white, assuming these colors are mutually exclusive?
   1. A) 0.10
   2. B) 0.25
   3. C) 0.50
   4. D) 0.60
3. In a genetics experiment, the probability of an offspring having trait A is 0.4, and the probability of having trait B is 0.3. If the probability of having both traits is 0.1, what is the probability of an offspring having either trait A or trait B?
   1. A) 0.6
   2. B) 0.7
   3. C) 0.8
   4. D) 0.9
4. A student is choosing a lab activity. The probability of choosing activity X is 0.5, and the probability of choosing activity Y is 0.4. The probability of choosing both is 0.2. What is the probability of choosing either activity X or Y?
   1. A) 0.7
   2. B) 0.9
   3. C) 1.1
   4. D) 0.2
5. If the probability of event M is $\frac{1}{4}$ and the probability of event N is $\frac{1}{3}$, and they are mutually exclusive, what is the probability of either M or N occurring?
   1. A) $\frac{1}{12}$
   2. B) $\frac{7}{12}$
   3. C) $\frac{2}{7}$
   4. D) $\frac{1}{6}$
6. In a bag of marbles, 20% are blue and 30% are green. If 10% are both blue and green, what is the probability of randomly selecting a marble that is either blue or green?
   1. A) 0.4
   2. B) 0.5
   3. C) 0.6
   4. D) 0.1
7. A researcher is studying two genes. The probability of a plant having gene P is 0.6, and the probability of having gene Q is 0.5. If the probability of having both genes is 0.3, what is the probability of a plant having either gene P or gene Q?
   1. A) 0.7
   2. B) 0.8
   3. C) 1.1
   4. D) 0.3