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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.


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?

Math diagram

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.

x = color Red Blue Others P ( x ) 1 6 1 6 4 6 Tokens 2 5 1

Use the weighted average formula.

E ( x ) = 2 1 6 + 5 1 6 + ( 1 ) 4 6 = 2 6 + 5 6 4 6 = 3 6 or 0.5

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.

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