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Cogito

Probability and Statistics · Chapter 3 · Lesson 3

Practice Worksheet

Expected Value

What you would average over the long run.

12 problems · about 21 minutes · TEKS P.S.2.C, S-MD.B.5

NameDate

Figure — use these to answer the problems

Give the outcomes different likelihoods. The expected value drifts toward whichever grows.
Win 101
Lose 29
Win1
Lose9
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Pays $40 with probability 0.1, else $0. Expected payout in dollars?

    Answer

  2. What makes a game fair?

    • The expected gain is zero.
    • Every outcome is equally likely.

  3. Pays $10 with probability 0.5, else $0. Expected payout in dollars?

    Answer

  4. Pays $100 with probability 0.01, else $0. Expected payout?

    Answer

  5. Expected payout $5, cost to play $5. Expected gain?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Is that game fair? 1 for yes, 0 for no.

    Answer

  2. Expected payout $3, cost $4. Expected gain in dollars?

    Answer

  3. Pays $6 with probability 0.5 and $2 with probability 0.5. Expected payout?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Which statements about expected value are true?

    • It is a long-run average
    • It may be a value that never actually occurs
    • It predicts the next single result
    • It is always positive
    • Tick every box that applies.

  2. Pays $50 with probability 0.02, else $0. Expected payout?

    Answer

  3. The Payout

    A game pays $20 with probability 0.25 and $0 otherwise. What is the expected payout, in dollars?

    Answerdollars

  4. The Die

    What is the expected value of one roll of a fair six-sided die?

    Answer