Expected value with calculated probabilities

The topic of  is under the Probability and statistics Math Mission. This exercise calculates expected values from theoretical probability situations.

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the expected value: This problem provides a chart or describes a situation with certain values. The student is expected to calculate the expected value and insert it into the provided space.Expcal1.png

Strategies
This exercise is hard to get accuracy badges because some of the probabilities can be subtle if you are not careful. The speed badges are also hard because there are few shortcuts on some of the problems.
 * 1) An expected value is found by taking the sum of the pairwise products of probabilities with payouts.
 * 2) All probabilities add to one, so if you can find all but one of the probabilities in a random variable, the last can be found by subtraction.
 * 3) There are several problems which include a chart and some situation where a person is '50% likely' to have something happen. These problems have probabilities that are always binomial in nature (like coin flips). If you know the first few binomials distributions you can use these probabilities with the payouts to get the answer a little more quickly.