Expected value with empirical probabilities

The topic of  is under the Probability and statistics 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 student is asked to select all the of the statements from a multiple select listing that are true about the experiment based on the data.Expemp1.png
 * 2) Predictive line chart: This problem describes a particular experiment from which it is possible to find the expected value. The student is then expected to create a line chart of the amount they expect to win based on number of additional trials they run.Expemp2.png
 * 3) Use expected value to find unknowns: This problem provides a chart with one or two missing pieces of information. The student is asked to take the information provided and use it to infer the missing information.Expemp3.png

Strategies
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.