Test questions for calculating theoretical probability

📚 Quick Study Guide

🔢 Theoretical Probability: The likelihood of an event happening based on mathematical calculations. It's calculated as: $P(Event) = \frac{Number \ of \ Favorable \ Outcomes}{Total \ Number \ of \ Possible \ Outcomes}$. 🎲 Sample Space: All possible outcomes of an experiment. For example, when rolling a six-sided die, the sample space is {1, 2, 3, 4, 5, 6}. ⚖️ Fairness: Assumes all outcomes are equally likely. For instance, a fair coin has a 50% chance of landing on heads or tails. 🎯 Independent Events: Events where the outcome of one does not affect the outcome of the other. The probability of two independent events A and B both occurring is: $P(A \ and \ B) = P(A) * P(B)$. 🤝 Mutually Exclusive Events: Events that cannot happen at the same time. The probability of either A or B occurring is: $P(A \ or \ B) = P(A) + P(B)$.

🧪 Practice Quiz

1. What is the theoretical probability of rolling an even number on a fair six-sided die?
   1. $\frac{1}{6}$
   2. $\frac{1}{3}$
   3. $\frac{1}{2}$
   4. $\frac{2}{3}$
2. A bag contains 5 red marbles and 3 blue marbles. If you randomly select one marble, what is the theoretical probability that it is blue?
   1. $\frac{3}{5}$
   2. $\frac{5}{8}$
   3. $\frac{3}{8}$
   4. $\frac{1}{2}$
3. What is the probability of flipping a fair coin and getting heads?
   1. 0
   2. $\frac{1}{4}$
   3. $\frac{1}{3}$
   4. $\frac{1}{2}$
4. A spinner has 4 equal sections labeled 1, 2, 3, and 4. What is the probability of spinning a 3?
   1. $\frac{1}{4}$
   2. $\frac{1}{2}$
   3. $\frac{3}{4}$
   4. 1
5. What is the probability of drawing an Ace from a standard deck of 52 cards?
   1. $\frac{1}{52}$
   2. $\frac{1}{26}$
   3. $\frac{1}{13}$
   4. $\frac{1}{4}$
6. Two fair dice are rolled. What is the probability that the sum of the numbers is 7?
   1. $\frac{1}{6}$
   2. $\frac{1}{12}$
   3. $\frac{7}{36}$
   4. $\frac{1}{2}$
7. A box contains 6 green balls and 4 yellow balls. What is the probability of randomly selecting a green ball?
   1. $\frac{2}{5}$
   2. $\frac{3}{5}$
   3. $\frac{1}{2}$
   4. $\frac{5}{6}$