Algebra 2 Test Questions: Mastering Theoretical & Experimental Probability

📚 Quick Study Guide

• 🎲 Theoretical Probability: The probability of an event based on mathematical reasoning. Formula: $P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$
• 🧪 Experimental Probability: The probability of an event based on data collected from experiments or observations. Formula: $P(A) = \frac{\text{Number of times the event occurs}}{\text{Total number of trials}}$
• 🧮 Sample Space: The set of all possible outcomes of an experiment.
• ✅ Independent Events: Events where the outcome of one does not affect the outcome of the other. $P(A \text{ and } B) = P(A) \cdot P(B)$
• ⛔ Dependent Events: Events where the outcome of one event affects the outcome of the other. $P(A \text{ and } B) = P(A) \cdot P(B|A)$, where $P(B|A)$ is the probability of B given that A has occurred.
• ➕ Mutually Exclusive Events: Events that cannot occur at the same time. $P(A \text{ or } B) = P(A) + P(B)$
• 🤝 Non-Mutually Exclusive Events: Events that can occur at the same time. $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$

🤔 Practice Quiz

1. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the theoretical probability of randomly selecting a red marble?
   1. $\frac{1}{2}$
   2. $\frac{3}{10}$
   3. $\frac{1}{5}$
   4. $\frac{1}{10}$
2. A coin is flipped 50 times, and it lands on heads 28 times. What is the experimental probability of landing on heads?
   1. $\frac{22}{50}$
   2. $\frac{14}{25}$
   3. $\frac{1}{2}$
   4. $\frac{28}{78}$
3. What is the probability of rolling a 4 on a six-sided die and then flipping a coin and getting tails?
   1. $\frac{1}{12}$
   2. $\frac{1}{4}$
   3. $\frac{1}{3}$
   4. $\frac{2}{3}$
4. A spinner has 8 equal sections, numbered 1 to 8. What is the probability of spinning a number greater than 5?
   1. $\frac{5}{8}$
   2. $\frac{1}{2}$
   3. $\frac{3}{8}$
   4. $\frac{1}{4}$
5. Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that both cards are aces?
   1. $\frac{1}{221}$
   2. $\frac{1}{13}$
   3. $\frac{1}{169}$
   4. $\frac{4}{52}$
6. A survey shows that 60% of students like pizza and 40% like burgers. 20% like both. What percentage of students like either pizza or burgers?
   1. 100%
   2. 80%
   3. 24%
   4. 60%
7. A bag contains 7 yellow balls and 3 green balls. If two balls are drawn at random without replacement, what is the probability that the first ball is yellow and the second is green?
   1. $\frac{7}{30}$
   2. $\frac{21}{100}$
   3. $\frac{1}{5}$
   4. $\frac{7}{10}$