The following spinner is used in a game that cost 3 to play

The following spinner is used in a game that cost $3 to play. Find the expected value if you win the amount the spinner is pointing to. I.E. if the spinner lands on a 4, you win $4.

Solution

Total different amount = 16

Probabilty that you win $1 = 4/16 = 1/4

Probabilty that you win $2 = 3/16

Probabilty that you win $3 = 3/16

Probabilty that you win $4 = 3/16

Probabilty that you win $5 = 3/16

Now total expected value will be:

E = 1*(4/16) + 2*(3/16) + 3*(3/16) + 4*(3/16) + 5*(3/16) - 3*1

E = -0.125

which means player will lose $0.125 every time he plays

	$1	$2	$3	$4	$5	wager
Expected value	1	2	3	4	5	-3
probability	4/16	3/16	3/16	3/16	3/16	1