Create the outcome table
List mutually exclusive outcomes, assign their stated gains or losses, and ensure the probabilities sum to one. Define monetary values consistently, including any costs that apply.
Probability & statistics / English
How To Calculate Expected Value
The Organic Chemistry Tutor · YouTube · 6:59
YouTube · The Organic Chemistry TutorOriginal video
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Calculate expected value from explicit outcome tables and scale an expectation across repeated units.
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0:00Create the outcome table1:30A two-outcome calculation6:00Expected profit is not a guaranteeLearning script
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List mutually exclusive outcomes, assign their stated gains or losses, and ensure the probabilities sum to one. Define monetary values consistently, including any costs that apply.
For the stated outcome values 500 and −100 with probabilities 0.2 and 0.8, the weighted mean is . This conclusion uses those specified outcome values.
The laptop example gives 40 with probability 0.97 and −500 with probability 0.03, so the mean is 23.8 per unit. Summing expectations gives 2380 for 100 such units, rather than a guaranteed realized profit.
Knowledge cards
A two-outcome calculation
For the stated outcome values 500 and −100 with probabilities 0.2 and 0.8, the weighted mean is . This conclusion uses those specified outcome values.
Expected profit is not a guarantee
The laptop example gives 40 with probability 0.97 and −500 with probability 0.03, so the mean is 23.8 per unit. Summing expectations gives 2380 for 100 such units, rather than a guaranteed realized profit.
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- Expectation ExplanationAt 0:00
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List mutually exclusive outcomes, assign their stated gains or losses, and ensure the probabilities sum to one. Define monetary values consistently, including any costs that apply. For the stated outcome values 500 and −100 with probabilities 0.2 and 0.8, the weighted mean is . This conclusion uses those specified outcome values. The laptop example gives 40 with probability 0.97 and −500 with probability 0.03, so the mean is 23.8 per unit. Summing expectations gives 2380 for 100 such units, rather than a guaranteed realized profit.
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