A game of chance involves rolling a 14-sided die once. If a number from 1 to 3 comes up, you win 2 dollars. If the number 4 or 5 comes up, you win 9 dollars. If any other number comes up, you lose. If it costs 5 dollars to play, what is your expected net winnings?

Ok so let's say that you have a 3/13 chance of winning $3 and a 2/13 chance of winning $10 and a 8/13 chance of winnning $0. 

Therefore if the dice is rolled 13 times, I am expected to win 3X$3 + 2X$10 = $29 

But I am paying $5 per roll so 13 rolls would cost me 13X$5 = $65 

So therefore my expected net winnings is $29-$65 = -$36 

I would lose $36 according to chance.
I hope this help's. Good luck!