How To Calculate Expected Value

The Organic Chemistry Tutor
30 May 202006:59
EducationalLearning
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TLDRThe video explains how to calculate expected value, which estimates how much money you can expect to win or lose on average per game or transaction. It provides two examples. First, it calculates the expected value for a game with a 20% chance of winning $500 and an 80% chance of losing $100. The expected value per game is $20. It then calculates the expected profit per laptop for a company that earns $40 per working laptop but loses $500 for each defective laptop, given a 3% defect rate. The expected value of profit per laptop is $23.80.

Takeaways
  • ๐Ÿ˜€ How to organize data for expected value problems in a table format
  • ๐Ÿ˜Š Calculate expected value using the formulas: EV = ฮฃ(probability x value)
  • ๐Ÿ“ Convert percentages to decimals when calculating probabilities
  • ๐Ÿ˜Ž Can estimate total earnings over multiple trials using expected value per trial
  • ๐Ÿ“Š Generate a table with outcomes, values, and probabilities for structured analysis
  • ๐Ÿ”ข Calculate expected value for both winning and losing outcomes
  • ๐Ÿค“ Apply expected value to estimate business profits and losses
  • ๐Ÿงฎ Use expected value to evaluate profit/loss per item sold
  • ๐Ÿ’ฐ Estimate total profit over number of items sold using per item expected value
  • โœ๏ธ Demonstrated expected value calculation on both gambling and business examples
Q & A

  • What are the two potential outcomes in the game Lisa plays?

    -The two potential outcomes are that Lisa wins the game or loses the game.

  • How much money does Lisa earn if she wins the game?

    -Lisa earns $500 if she wins the game.

  • What is Lisa's probability of winning the game?

    -Lisa has a 20% probability of winning the game.

  • How do you calculate expected value?

    -To calculate expected value, multiply the value of each outcome by its probability, and then sum those numbers.

  • What is the expected value per game for Lisa?

    -The expected value per game for Lisa is $20.

  • How much would Lisa expect to earn if she played 10 games?

    -If Lisa played 10 games, she would expect to earn $200.

  • What are the two potential laptop outcomes for company XYZ?

    -The two potential laptop outcomes are a working laptop or a defective laptop.

  • What is the probability that company XYZ produces a defective laptop?

    -Company XYZ has a 3% probability of producing a defective laptop.

  • What is the expected profit per laptop for company XYZ?

    -The expected profit per laptop for company XYZ is $23.80.

  • How much profit would company XYZ expect with 100 sold laptops?

    -If company XYZ sold 100 laptops, they would expect a profit of $2,380.

Outlines
00:00
๐Ÿ˜Š Calculating Expected Value for Winning a Single Game

This paragraph explains how to calculate the expected value for winning a single game. It goes through an example game where Lisa has a 20% chance to win $500 and 80% chance to lose $100. By multiplying the value of each outcome by its probability, the expected value per game is calculated as $20. This is then used to estimate total expected winnings if Lisa plays 10 or 100 games.

05:01
๐Ÿ’ก Calculating Expected Profit Per Laptop Sold

This paragraph provides an example of calculating expected profit per laptop sold for company XYZ. There is a 97% chance of making a working laptop that nets $40 profit, and a 3% chance of a defective laptop that loses $500. By multiplying the profit/loss values by the probabilities, the expected value or average profit per laptop is $23.80. This can then estimate total profit for any number of laptops sold.

Mindmap
Keywords
๐Ÿ’กoutcomes
Outcomes refer to the possible results or end states in a probabilistic situation. In the video, the two main outcomes are Lisa winning or losing the game. Identifying the outcomes is an important first step in calculating expected values.
๐Ÿ’กvalue
Value refers to the gain or loss associated with each outcome. For example, if Lisa wins she gains $500, while if she loses she loses $100. Quantifying these values for each outcome allows computation of expected values.
๐Ÿ’กprobability
Probability represents the likelihood of each outcome occurring, expressed as a decimal between 0 and 1. Knowing the probabilities for each outcome is essential for computing the expected value.
๐Ÿ’กexpected value
The expected value is the probability-weighted average value over all potential outcomes. It represents the mean value one would expect over many trials. Calculating expected value was the main goal of the numerical examples.
๐Ÿ’กprofit
In the second example, profit refers to the money earned by the laptop company on each working laptop sold, which was $40. This is contrasted with the $500 loss for each defective laptop.
๐Ÿ’กdefective
A defective laptop refers to one that has to be returned due to some problem, which costs the company $500. The probability of producing a defective laptop was a key input for determining expected profit per laptop.
๐Ÿ’กformula
The video emphasizes the formula for computing expected value: Multiply each outcome value by its respective probability and sum over all outcomes. This formed the basis for the numerical calculations.
๐Ÿ’กearnings
Earnings represent the total amount of money gained over multiple instances of an uncertain situation. For example, expected earnings from 10 games would be 10 times the expected value per game.
๐Ÿ’กloss
Loss represents negative value, such as the $500 loss when the company produces a defective laptop. Incorporating losses is key for accurately determining expected values.
๐Ÿ’กestimate
A central purpose of expected value is to estimate typical outcomes over many trials. By extension, expected values allow estimation of total earnings or profits over a given number of occurrences.
Highlights

Organizes data in a table with outcomes, values, and probabilities.

Calculates expected value by multiplying outcome values by their probabilities.

Converts percentages to decimals by dividing by 100.

Expected value allows estimating total earnings from multiple games.

Company profit and loss outcomes for working and defective laptops.

Probability of defective laptops used to calculate probability of working ones.

Expected profit per laptop found by multiplying outcomes by probabilities.

Total expected profit calculated from expected profit per item.

Table organized with outcomes, values, probabilities for game scenario.

Percentage converted to decimal by dividing by 100.

Expected value allows estimating earnings over multiple games.

Losses represented by negative values.

Sums the expected values of winning and losing to get overall value.

Uses same process of calculating expected value for company laptop scenario.

Expected profit per laptop allows estimating total profit from number sold.

Transcripts

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