Expected Value Practice

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What is Expected Value?

Back

Expected Value (EV) is a calculated average of all possible outcomes of a random variable, weighted by their probabilities. It represents the long-term average if an experiment is repeated many times.

Tags

CCSS.HSS.MD.A.2

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How do you calculate Expected Value?

Back

To calculate Expected Value, multiply each possible outcome by its probability and sum all these products. Formula: EV = Σ (outcome × probability).

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CCSS.HSS.MD.A.2

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What is the Expected Value of a random variable with outcomes 1, 2, and 3, with probabilities 0.2, 0.5, and 0.3 respectively?

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EV = (1 × 0.2) + (2 × 0.5) + (3 × 0.3) = 0.2 + 1.0 + 0.9 = 2.1.

Tags

CCSS.HSS.MD.A.2

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What does a higher Expected Value indicate?

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A higher Expected Value indicates a more favorable outcome in terms of potential gains or benefits when making decisions.

Tags

CCSS.HSS.MD.B.5B

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What is the Expected Value of a household with 30% having 1 child, 43% having 2 children, and 27% having 3 children?

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EV = (1 × 0.3) + (2 × 0.43) + (3 × 0.27) = 0.3 + 0.86 + 0.81 = 1.97.

Tags

CCSS.HSS.MD.A.2

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What is Return on Investment (ROI)?

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Return on Investment (ROI) is a measure used to evaluate the efficiency of an investment, calculated as (Net Profit / Cost of Investment) × 100.

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CCSS.HSS.MD.B.6

CCSS.HSS.MD.B.7

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How do you determine which investment option has the greatest ROI?

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Compare the ROI percentages of each option. The option with the highest percentage is considered to have the greatest Return on Investment.

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What is the Expected Value of a game where you win $10 with a probability of 0.5 and lose $5 with a probability of 0.5?

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EV = (10 × 0.5) + (-5 × 0.5) = 5 - 2.5 = 2.5.

Tags

CCSS.HSS.MD.B.5A

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What is the significance of the Expected Value in decision-making?

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Expected Value helps in making informed decisions by providing a statistical basis for evaluating potential outcomes and risks.

Tags

CCSS.HSS.MD.B.5B

Front

What is a probability table and how is it used?

Back

A probability table lists outcomes and their associated probabilities, helping to visualize and calculate Expected Values more easily.

Tags

CCSS.HSS.MD.A.2