1.The game involves using two 10 sided dice with faces numbered 1 through 10.your interviewer tells you that the game costs $1 to play and it has an expected value of 47 cents for every dollar spent.Use the following payouts to determine the expected value of the game.Do you agree with your co-worker's assertion?

Roll Winnings

Sum of 19 $5

Sum of 17 $3

Sum of 15 $2

Sum of 13 $1

Doubles $.5

Other $0

Below are my answers I need help understanding the answer for other with a zero payout.

It leaves 70 probabilities there would be no payout.

Sum of 19 has 2 ways to roll a (9,10) or a (10,9) with 2 out of 100 or 2/100 =.02

.02*19=.385*.02=.10

Sum of 17 has 4 ways to roll (10,7) (7,10) (8,9) (9,8) with 4 out of 100 or 4/100 =.04

.04*17=.683*.04=.12

Sum of 15 has 6 ways to roll (10,5) (5,10) (9,6) (6,9) (8,7) (7,8) with 6 out of 100 or 6/100=.06

.06*15= .902*.06=.12

Sum of 13 has 8 ways to roll (10,3) (3,10) (9,4) (4,9) (8,5) (5,8) (7,6) (6,7) with 8 out of 100=.08

.08*13=1.04 1*.08=.08

Sum of doubles has 10 ways to roll (1,1) (2,2) (3,3) (4,4) (5,5) (6,6) (7,7) (8,8) (9,9) (10,10) with 10 out of 100 or 10/100 or 1/10 =.10.10*10=1.00 .50*.10=.05

That is 30 rolls out of 100 which leaves 70 rolls falling under other and those has no winnings.(2+4+6+8+10=30) 10x10=100 100-30=70.The probability of the others 70/100 or .70