Question

A large spinning wheel has 20 pie slices of different colors. There are 7 green slices, 4 red slices, and the rest are black. If you spin the wheel and the pointer stops at green you win $2, stops at red you win $5, stops at black you win nothing. If you are charged $3 to play this game then how much is the expected value if you played 10 times?

Answer 1

Expected value is $13

Explanation:

It is given that number of slices in spinning wheels =20

Number of green slice = 7

Number of red slice = 4

It is given that when green and red slice comes there is a win

Probability of outcome of green slice
`=(7)/(20)`

Probability of outcome of red slice
`=(4)/(20)`

It is given that when green slice comes win price is $2 and when red slice come price $5

So winning price

`=(7)/(20)* 2+(4)/(20)* 5=1.7`

Charge of each play is $3

So expected value if he plays one times =$1.7 - $3 = -$1.3

He plays 10 times

Therefore total expected values = 10×-$1.3= $13