Use the average to make a decision
| Option | What you receive |
|---|---|
| A: guaranteed | €50 every time |
| B: gamble | 30% chance of €200; otherwise €0 |
Which would you choose?
Compare the guaranteed €50 with the gamble.
Step by step
- Find the gamble’s average prize.
- Choose B for the higher average (€60). Or choose A for a guaranteed €50 in one play.
Final answer
Either choice can be reasonable. Give the option and a reason: higher average or lower risk.
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Your current score can affect the gain
| Result | Change in points: Y | Chance |
|---|---|---|
| Win 4 points | +4 | 0.5 |
| Lose your current x points | −x | 0.5 |
When does playing lose points on average?
You have x points. Y is the change in your score. Find when E(Y) is negative.
Step by step
- Multiply each change by its chance and add.
- For example, with 6 points, the average change is 2 − 3 = −1 point.
- Find when the average change falls below zero.
Final answer
With more than 4 points, playing loses points on average. At exactly 4 points, the average change is zero.
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Exam-style question
Try it, then check
You have x points. You gain 6 with probability 0.5, or lose all x with probability 0.5. Find E(Y), then when it is negative. [4]
Step by step
- Y is the change: +6 or −x.
- Set the average change below zero.
Final answer
Continuing loses points on average when x > 6.