Expected Value Probability Grade 12 Essential Math Expected
Expected Value Probability Grade 12 Essential Math
Expected Value • Probability can be used to find expected value • Expected value can help us predict winnings or losses • It is frequently used by insurance companies and businesses • In many games, you pay a given amount to play. • If you win the game, you receive a payout. • But is the game worth playing? Does the amount you could win sound too good to be true?
Activity • You need to repeat this activity as many times as needed until a definite pattern becomes clear • One person will act as the banker and will have 15 of the pennies • The other people will have 10 pennies. • The player must pay the banker 1 penny each time the game is played. • If the player draws a spade, the banker pays them 3 pennies. • Play for at least 10 games. How much money does each player have?
Questions 1. What happened in each of the groups? 2. Would you play this game with money? Why? 3. Does the player have much of an expectation of winning at this game? Why or why not?
Expected Value •
Example • Using the game from the activity, find the expected value of the game. • How much would you expect to win/lose if you played 100 games?
Example • A card game has five cards, one of which is the winner. The game costs $1. 00 to play. If you select the correct card, you win $4. 00. Calculate the expected win/loss. Interpret the meaning of this number.
Example • Rachel owns a window cleaning company. She is considering putting in a bid for a contract. She calculates the expected value to be $425. Interpret the meaning of the expected value. Should she bid on the contract?
Example • Based on past experience, a building contractor estimates that the probability of winning a contract is 0. 30. • The contract is worth $25, 000 profit and she knows it will cost her $2, 400 to prepare a contract proposal. 1. Find the expected value of the contract proposal. 2. Is it financially a good idea for her to bid on the contract? 3. What other factors might she consider before making a decision?
Example when there is more than one probability • “Pick the Marble” is a game that involves picking one marble out of a bag. In the bag, 32% of the marbles are red, 4% of the marbles are green, and 64% of the marbles are blue. It costs $2 to play, and the prices are listed. Colour Probability of Winning Prize Red 32% Stuffed animal worth $10 Green 4% Stuffed animal worth $15 Blue 64% Nothing • Calculate the expected value for the game.
- Slides: 10