Question

Suppose that in a certain game, a player rolls an ordinary six-sided number cube. If the cube lands on 6, the player is paid $4. If the cube lands on any other number, the player loses $1. What is the player’s mathematical expectation?

Answer 1

`-$0.17`

Explanation:

What we do with questions of this sort is to sum up each result multiplied by it's probability.

We have two results to look at.

The first is winning $4 when the cube lands on a 6. There is a `1/6` probability of a fair standard cube landing on any set value (such as our 6). And so the expected value of this is:

`$4xx1/6=$4/6`

The other result is landing on any other value and losing $1. There is a `5/6` probability of not landing on the 6 and so the expected value of this is:

`-$1xx5/6=-$5/6`

And now we sum it all up:

`$4/6-$5/6=-$1/6~~-$0.17`

And so on each throw of the die, our expectation is to lose $0.17.