Question

calculate the expected value of the carnival game in the activity. Does the school make money or lose money at this booth? Toss Away! roll 2 dice…- If you roll 2 odd numbers, like a 3 or a 5, you get $2.- If you roll a 2 even numbers, like a 4 or a 6, you get $2 otherwise, you get nothing.

Answer 1

The expected value is calculated by:

`E(x)=x_1p_1+x_2p_2+x_3p_(3\ldots)`

x represents the value and p the probability.

For this problem we need to know how many possibilities for you to roll 2 odd numbers, 2 even numbers and to get nothing.

As can be seen in the diagram above, the probability of obtaining two even numbers is:

`P(even)=(9)/(36)=0.25`

And for two odd numbers:

`P(odd)=(9)/(36)=0.25`

And to get nothing:

`P(nothing)=(18)/(36)=0.5`

Then the expected value must be:

`E(x)=2\cdot0.25+2\cdot0.25-1\cdot0.5`
`E(x)=0.5`

At this booth the school makes money because the expected value for the player is less than what is worth to play.