expected value examples high school math

📚 Quick Study Guide

• 🎲 Expected Value (EV) is the average outcome of a probabilistic event.
• 🔢 Formula: $EV = \sum (x_i * P(x_i))$, where $x_i$ is each outcome and $P(x_i)$ is its probability.
• 💰 EV can be positive (indicating a potentially profitable scenario), negative (indicating a potential loss), or zero (indicating a fair game).
• 💡 To calculate EV, multiply each possible outcome by its probability and then add all those products together.
• 📊 EV is used in various fields like finance, insurance, and gambling to make informed decisions.

🤔 Practice Quiz

1. What does Expected Value (EV) represent?
   1. The most likely outcome.
   2. The average outcome.
   3. The worst possible outcome.
   4. The best possible outcome.
2. A game has two outcomes: winning $10 with a probability of 0.4, and losing $5 with a probability of 0.6. What is the expected value?
   1. $1
   2. $2
   3. $4
   4. -$1
3. If the expected value of a game is zero, what does this indicate?
   1. The game is guaranteed to break even.
   2. The game is unfair.
   3. The game is fair.
   4. The game always results in a loss.
4. What is the formula for calculating expected value?
   1. $EV = \sum (x_i + P(x_i))$
   2. $EV = \sum (x_i * P(x_i))$
   3. $EV = \frac{\sum x_i}{\sum P(x_i)}$
   4. $EV = x_1 * x_2 * ... * x_n$
5. In a raffle, 1 ticket wins $500, and 10 tickets win $50 each. If 1000 tickets are sold, what is the expected value of buying one ticket?
   1. $0.50
   2. $1.00
   3. $1.50
   4. $2.00
6. A coin is flipped. If it lands heads, you win $2. If it lands tails, you lose $1. What is the expected value?
   1. $0.25
   2. $0.50
   3. $1.00
   4. $1.50
7. Why is understanding expected value important in real-world scenarios?
   1. It helps in making informed decisions in finance.
   2. It helps in understanding insurance policies.
   3. It helps in evaluating gambling odds.
   4. All of the above.