MediumStatistics & Data ScienceHigh School (9–10)High School (11–12)UndergraduateGeneralStatistics Basics › Probability and ChanceStatistics Basics › Tables and GraphsNumerical
A made-up spinner has 10 equal sectors. One sector pays a top prize of W tokens, three sectors pay…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A made-up spinner has equal sectors. One sector pays a top prize of tokens, three sectors pay tokens each, and the rest pay nothing. A play costs tokens. Find the expected prize from the three small sectors, and the top prize that makes the game fair. Then find the expected gain per play if the top prize is tokens.
Need a reminder? The key ideaShow
Expected value: , the long-run average. Expected gain is the expected prize minus the cost. A fair game has an expected gain of .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Small sectors. tokens.
Step 2. Fair top prize. , so and tokens.
Step 3. A top prize of 12. Expected prize: tokens. Expected gain: tokens.
Answer: tokens, tokens and tokens. With a top prize of tokens the game favours the player.
Discussion (0)
Log in to join the discussion.
Loading…