Quiz answers: Independent events probability multiplication rule

📚 Quick Study Guide

• 🎲Independent Events: Two events are independent if the outcome of one does not affect the outcome of the other.
• ➕ Multiplication Rule: For independent events A and B, the probability of both A and B occurring is: $P(A \text{ and } B) = P(A) \times P(B)$
• 📑 Extension: This rule can be extended to any number of independent events. For example, for three independent events A, B, and C: $P(A \text{ and } B \text{ and } C) = P(A) \times P(B) \times P(C)$
• 💡 Key Assumption: The multiplication rule *only* applies when events are independent. If events are dependent, a different rule is needed.

Practice Quiz

1. What is the probability of rolling a 4 on a fair six-sided die and then flipping a coin and getting heads?
   1. $\frac{1}{12}$
   2. $\frac{1}{2}$
   3. $\frac{1}{6}$
   4. $\frac{1}{3}$
2. A bag contains 5 red marbles and 3 blue marbles. You draw one marble, replace it, and then draw another. What is the probability of drawing a red marble both times?
   1. $\frac{25}{64}$
   2. $\frac{5}{8}$
   3. $\frac{10}{16}$
   4. $\frac{9}{64}$
3. Event A is rolling a number greater than 2 on a six-sided die. Event B is flipping a coin and getting tails. What is P(A and B)?
   1. $\frac{1}{3}$
   2. $\frac{2}{3}$
   3. $\frac{1}{6}$
   4. $\frac{4}{12}$
4. A spinner has 4 equal sections, numbered 1 to 4. What is the probability of spinning a 3, and then spinning a 1?
   1. $\frac{1}{16}$
   2. $\frac{1}{4}$
   3. $\frac{1}{8}$
   4. $\frac{1}{2}$
5. You have two decks of cards. You draw one card from each deck. What is the probability of drawing an Ace from both decks?
   1. $\frac{1}{52}$
   2. $\frac{1}{169}$
   3. $\frac{2}{52}$
   4. $\frac{1}{26}$
6. A coin is flipped three times. What is the probability of getting heads all three times?
   1. $\frac{1}{8}$
   2. $\frac{1}{2}$
   3. $\frac{3}{8}$
   4. $\frac{1}{4}$
7. A baseball player has a batting average of 0.300. What is the probability that they will get a hit in two consecutive at-bats, assuming each at-bat is independent?
   1. 0.09
   2. 0.6
   3. 0.3
   4. 0.03