Expected value with empirical probabilities
Expected-value-with-empirical-probabilities 256
Exercise Name: Expected value with empirical probabilities
Math Missions: High school statistics and probability Math Mission
Types of Problems: 3

The Expected value with empirical probabilities exercise appears under the High school statistics and probability Math Mission. This exercise works with empirical probabilities from an experiment to determine answers about expected results of the experiment.

Types of Problems

There are three types of problems in this exercise:

  1. Select true statements: This problem provides a chart of recorded data from an experiment. The user is asked to select all the of the statements from a multiple select listing that are true about the experiment based on the data.

    Select true statements

  2. Predictive line chart: This problem describes a particular experiment from which it is possible to find the expected value. The user is then expected to create a line chart of the amount they expect to win based on number of additional trials they run.

    Predictive line chart

  3. Use expected value to find unknowns: This problem provides a chart with one or two missing pieces of information. The user is asked to take the information provided and use it to infer the missing information.

    Use expected value to find unknowns


This exercise is medium to get accuracy badges because the techniques are not necessarily complicated, but they do call back to some previous material such as systems of equations. Speed badges are medium because some problems take work to get the answers and others are pretty fast.

  1. The formula for expected value it the sum of the pairwise products of probabilities and payouts.
  2. Calculator programs should be designable for Use expected value to find unknowns.
  3. You do not need to actually calculate probabilities to do all the multiple select answers. Some are able to be answered by comparing relative sizes of the values.
  4. The Predictive line chart problem seems to use nice numbers so graphing is simpler. The result should be a straight line through the origin as soon as you can figure out one point on the line.

Real-life Applications

  1. Probability, along with decimals, percents, and fractions are used to determine the probability of a basketball player making a shot.
  2. Data and statistics appear in news reports and in the media every day.
  3. Many of the problems in this exercise could be viewed as real-life applications.
  4. Statistics can be seen more frequently than calculus in every day life.

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