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Expected value

This resource explores the concept of expected value through various practical examples. Learn how to calculate the expected average from rolling a six-sided die, including scenarios with loaded dice. Discover how to compute GPA based on letter grades and their numerical values. Analyze survey data to find averages and learn to assess expected monetary gains from gift card sales. Each example emphasizes the role of probabilities and demonstrates how to arrive at a weighted average, reinforcing the significance of expected value in decision-making.

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Expected value

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  1. M408 Probability Unit Expected value

  2. Example 1 – • You have a six-sided die with faces of 1, 2, 3, 4, 5, and 6. If you roll the die several times, what would you expect the average of your rolls to be?

  3. Example 2 – • Suppose you have a ‘loaded’ die. It is designed such that the number ‘6’ appears 1/3 of the time, a ‘5’ appears 1/3 of the time, and 1, 2, 3, 4 have equal chances of appearing. • If you roll the die several times, what would you expect the average of your rolls to be?

  4. Expected Value = • Must involve numerical outcomes. • Multiply each outcome by its probability. • Add all the products. • Represents a ‘weighted’ average (after several trials). • Sum of probabilities = 1

  5. Example 3 – In four years at Fremd, you got an A in 15% of your classes, a B in 30% of your classes, a C in 40%, a D in 10%, and an F in 5% of your classes. What is your GPA? (When calculating GPA, A = 4, B = 3, C = 2, D = 1, F = 0)

  6. Example 4 – The table shows the number of siblings that students have, based on a survey. What is the average number of siblings for respondents in this survey?

  7. Example 5 – You took a survey, asking “How many hours of homework do you do each night?” You lost some of the data! Can you still determine the expected number of hours of homework done each night?

  8. Example 6 – I have 20 gift cards. I am selling them for three dollars each. Two of the cards have $20 value, five of the cards have $10 value, and the rest have no money. If you buy a gift card from me, what is your expected net monetary gain?

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