Independent probability events explained with simple examples

📚 Quick Study Guide

• 🔢 Independent events are 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: $P(A \text{ and } B) = P(A) \times P(B)$.
• 🪙 Examples include flipping a coin multiple times or rolling a die and then flipping a coin.
• 💡 Remember to multiply the probabilities to find the combined probability.

🎯 Practice Quiz

1. What is the probability of flipping a fair coin and getting heads, and then rolling a fair six-sided die and getting a 4?
   1. $\frac{1}{12}$
   2. $\frac{1}{2}$
   3. $\frac{1}{6}$
   4. $\frac{1}{8}$
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. $\frac{25}{49}$
   4. $\frac{10}{16}$
3. Event A is rolling a 3 on a six-sided die. Event B is spinning a spinner with 4 equal sections (red, blue, green, yellow) and landing on blue. What is $P(A \text{ and } B)$?
   1. $\frac{1}{24}$
   2. $\frac{1}{10}$
   3. $\frac{1}{3}$
   4. $\frac{1}{4}$
4. A coin is flipped three times. What is the probability of getting heads each time?
   1. $\frac{1}{8}$
   2. $\frac{1}{2}$
   3. $\frac{3}{2}$
   4. $\frac{1}{6}$
5. You have two independent events. Event X has a probability of 0.4, and Event Y has a probability of 0.7. What is the probability of both X and Y happening?
   1. 0.28
   2. 1.1
   3. 0.11
   4. 0.028
6. A basketball player makes 60% of their free throws. What is the probability they make two free throws in a row?
   1. 36%
   2. 60%
   3. 120%
   4. 30%
7. A random number generator selects a number from 1 to 10. What is the probability it selects an even number, and then (after resetting) selects the number 5?
   1. $\frac{1}{10}$
   2. $\frac{1}{4}$
   3. $\frac{1}{5}$
   4. $\frac{1}{20}$