Quiz yourself: Basic compound events in math

📚 Quick Study Guide

• 🔢 A compound event is an event that consists of two or more simple events.
• 🎲 When calculating probabilities of compound events, it's crucial to determine if the events are independent or dependent.
• ➕ For mutually exclusive events (events that cannot occur at the same time), the probability of either event occurring is the sum of their individual probabilities: $P(A \cup B) = P(A) + P(B)$.
• ➖ For non-mutually exclusive events, we subtract the probability of both events occurring to avoid double-counting: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.
• 🎯 Independent events are events where the outcome of one does not affect the outcome of the other. The probability of both occurring is the product of their individual probabilities: $P(A \cap B) = P(A) \cdot P(B)$.
• 🔗 Dependent events are events where the outcome of one affects the outcome of the other. The probability of both occurring is $P(A \cap B) = P(A) \cdot P(B|A)$, where $P(B|A)$ is the probability of B given that A has occurred.
• 📊 Conditional probability is calculated as: $P(A|B) = \frac{P(A \cap B)}{P(B)}$.

📝 Practice Quiz

1. A bag contains 3 red marbles and 4 blue marbles. You draw one marble, replace it, and draw another. What is the probability of drawing a red marble then a blue marble?
   1. $\frac{3}{7}$
   2. $\frac{4}{7}$
   3. $\frac{12}{49}$
   4. $\frac{7}{14}$
2. A spinner has 8 equal sections, numbered 1 to 8. What is the probability of spinning an even number, then an odd number?
   1. $\frac{1}{4}$
   2. $\frac{1}{2}$
   3. $\frac{1}{8}$
   4. $\frac{3}{8}$
3. A card is drawn from a standard deck of 52 cards. What is the probability of drawing a heart or a king?
   1. $\frac{17}{52}$
   2. $\frac{4}{13}$
   3. $\frac{13}{52}$
   4. $\frac{1}{4}$
4. A jar contains 5 green balls and 3 yellow balls. Two balls are drawn without replacement. What is the probability that both balls are green?
   1. $\frac{5}{14}$
   2. $\frac{25}{64}$
   3. $\frac{10}{56}$
   4. $\frac{3}{28}$
5. What is the probability of rolling a 4 on a six-sided die and flipping heads on a fair coin?
   1. $\frac{1}{12}$
   2. $\frac{1}{2}$
   3. $\frac{1}{6}$
   4. $\frac{1}{3}$
6. Two dice are rolled. What is the probability that the sum of the numbers is 7 or 11?
   1. $\frac{2}{9}$
   2. $\frac{1}{6}$
   3. $\frac{7}{36}$
   4. $\frac{1}{9}$
7. In a class, 60% of the students like math, and 70% like science. 40% like both. What percentage of students like math or science?
   1. 90%
   2. 50%
   3. 30%
   4. 75%