Expected Value Worksheet
Grade 12 Math worksheet on Expected Value, covering calculations and applications in probability and statistics.
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Expected Value Worksheet
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Read each question carefully and answer to the best of your ability. Show all work for calculation problems.
1. What does the expected value of a random variable represent?
The most likely outcome of an experiment.
The average value of the outcomes over many trials.
The maximum possible outcome in a single trial.
The probability of a specific outcome occurring.
2. In a game, you win $10 if you roll a 6 on a standard six-sided die, and lose $2 otherwise. What is the expected value of playing this game once?
$0.00
$1.00
-$0.33
$2.00
3. The formula for expected value E(X) is the sum of each outcome multiplied by its .
4. If the expected value of a game is negative, it means that, on average, you can expect to money over many plays.
5. A company is considering investing in a new project. There is a 40% chance of making a profit of $50,000, a 30% chance of breaking even, and a 30% chance of losing $20,000. Calculate the expected monetary value of this project.
6. The expected value must always be one of the possible outcomes of the random variable.
True
False
7. A carnival game involves spinning a wheel with 8 equally likely sections. Four sections award $0, three sections award $5, and one section awards $20. It costs $3 to play the game. Should you play this game? Justify your answer using expected value.
8. Consider a random variable X with the following probability distribution:
P(X=1) = 0.2
P(X=2) = 0.5
P(X=3) = 0.3
Represent the expected value of X on a number line.