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Expected value
Expected value 256
Description
Exercise Name: Expected value
Math Missions: High school statistics and probability Math Mission
Types of Problems: 3

The Expected value exercise appears under the High school statistics and probability Math Mission. This exercise calculates expected values for random variables and uses them to help assist decision making.

Types of Problems

There are three types of problems in this exercise:

  1. Decide to play game: This problem describes a game with payouts and probabilities. The user is supposed to decide whether or not they should play the game based on expected value.
    Exval1

    Decide to play game

  2. Expected winnings: This problem describes a game where one can win a certain amount of money if an event occurs. The user is asked to calculate the actual expected winnings from playing the game.
    Exval2

    Expected winnings

  3. Expected value: This problem describes a situation where there is not money involved, but rather just a situation. The user is asked to find the expected value of the situation.
    Exval3

    Expected value

Strategies

This exercise is medium to get accuracy badges because users need to make sure they are familiar with probability and the calculation of expected value. Once this is familiar speed badges seem easy because the problem types are pretty easy to calculate.

  1. To find expected value, multiply the probability by the payout and add these pairwise products together.
  2. An expected value that is positive is good, whereas negative is bad (as a player).
  3. Users do not need to subtract the value of the ticket at the beginning, they can calculate expected winnings and then subtract the ticket. This can be faster because the amount of winnings if the user's lose is then interpreted as $0.
  4. The expected value of a die roll is half the sum of 1 and the number of faces on the die.

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