Mathematics
Grade 11
15 min
Choose the better bet
Choose the better bet
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Calculate the expected value of a single bet or game of chance.
Compare the expected values of two or more different bets to determine the most mathematically favorable option.
Define and calculate the probabilities of all possible outcomes in a given scenario.
Analyze a game of chance to determine if it is fair, favorable, or unfavorable to the player.
Apply the concept of expected value to make informed decisions in problems modeling real-world scenarios.
Interpret the meaning of positive, negative, and zero expected value in the context of a bet.
Would you rather have a 50% chance to win $100 or a 10% chance to win $500? 🤔 This lesson gives you the mathematical tools to answer that question definitively!
This tutorial introduces the powerful concept...
2
Key Concepts & Vocabulary
TermDefinitionExample
ProbabilityA numerical measure of the likelihood that a specific event will occur, expressed as a number between 0 (impossible) and 1 (certain).The probability of rolling a 4 on a standard six-sided die is 1/6, as there is one favorable outcome (rolling a 4) out of six total possible outcomes.
Random Variable (X)A variable whose value is a numerical outcome of a random phenomenon. In our context, this is often the amount of money you can win or lose.In a game where you win $10 for heads and lose $5 for tails, the random variable X can take on the values +$10 or -$5.
Expected Value (E(X))The long-term average outcome of an experiment if it is repeated many times. It is a weighted average of all possible values of a random variable, with the weights being their respect...
3
Core Formulas
Expected Value Formula
E(X) = \sum_{i=1}^{n} x_i P(x_i)
To find the expected value, you multiply each possible outcome value (x_i) by its probability (P(x_i)) and then sum all of those products together. This is the central formula for choosing the better bet.
Net Winnings Calculation
Net Value (x_i) = Payout_i - Cost_{play}
Before using the Expected Value formula, you must calculate the net value for each outcome. This ensures you are evaluating the actual profit or loss, not just the prize amount.
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Easy
According to the tutorial, what is the primary purpose of calculating the Expected Value, E(X), of a game of chance?
A.To determine the highest possible single prize you can win.
B.To find the average outcome you can expect if you play the game many times.
C.To calculate the exact amount of money you will win or lose on the next play.
D.To determine the probability of winning any prize.
Easy
A game costs $5 to play. One of the winning outcomes gives a prize of $20. What is the 'Net Winnings' (x_i) for this specific outcome that should be used in the Expected Value formula?
A.$20
B.$25
C.-$5
D.$15
Easy
A game is described as 'fair'. What does this imply about its Expected Value, E(X)?
A.E(X) is positive (E(X) > 0)
B.E(X) is negative (E(X) < 0)
C.E(X) is zero (E(X) = 0)
D.E(X) is equal to the cost of playing.
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing Free