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Expected value with calculated probabilities
Expected-value-with-calculated-probabilities 256
Description
Exercise Name: Expected value with calculated probabilities
Math Missions: High school statistics and probability Math Mission
Types of Problems: 1

The Expected value with calculated probabilities exercise appears under the High school statistics and probability 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 user is expected to calculate the expected value and insert it into the provided space.
    Expcal1

    Find the expected value

Strategies

This exercise is hard to get accuracy badges because some of the probabilities can be subtle if users 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 users 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 users know the first few binomials distributions they can use these probabilities with the payouts to get the answer a little more quickly.

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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