Using Expected Values to Make Decisions
The expected value of a random variable can be used to make decisions, for example about whether to place a bet or play a game.
Example:
At a school fair, you are given a number of tokens. In one stall at the fair, there is a spinner with 6 sectors. If the spinner lands on a red sector, you win 2 tokens. If you land on a blue sector, you win 5 tokens. If you land on any other sector, you lose 1 token.
Are you better off playing this game or not?
The spinner has 6 sectors and each is an equally likely possibility.
Sample space is {red sector, blue sector, 4 other sectors}
Write the probability distribution for a single spin of spinner and the amount of tokens you win.
Use the weighted average formula.
So, the expected value is 0.5 tokens, which is positive. In other words, on average, you get 0.5 token per spin, so you are better off playing this game.
