What Is The Expected Value?

now you know 3 cards and 49 are in the deck

a)you can't hit a pair over nines

you'll hit two pair if one of the next card is a 4 a 6 or a 8 so it is 9 cards out of 49 this means 18.4% and the fifth card is another one of the different ranked 6 cards so 6 out of 48 12.5% this means you'll hit a two pair in the 0.184*0.125=2.3%

you'll hit a 3 of a kind if the two following cards have both the same rank of one of yours this means 9 out of 49 times 2 out of 48 so the 0.8%

you'll hit a straight if one of the following card is a 7 and the second is a 5 or a 5 and the last card is a 7 so we have 8 out of 49 times 4 out of 48 so the 1.4%

with infinite coins you'll win the 2.3% of 3 plus the 0.8% of 5 and the 1.4% of 10 for a total of 0.25 coins so if you pay 1 coin to see at the last two cards your expected value is 0.25-1= -0.75 coins this means that every times you play you are loosing money

b)you can hit a pair of queens with two cars so this means 3/49 + 46/49 * 3/48 = 12%

but you can't hit a straight so this means with infinite tries you'll have the 12% of 2 + 2.3% of 3 + 0.8% of 5 = 0.35 coins with an EV of 0.35 - 1 = -0.65 you loose money but not as fast as in the case a

c) you can have two pair with a 4 in the last two cards this means 3/49 + 46/49 * 3/48 = 12%

you can hit a three of a kind wit a six in the other two cards this means 2/49 + 47/49 * 2/48 = 8%

you can hit a full house with a 6 and a 4 or a 4 and a 6 or two 4s this means 2/49 * 3/48 + 3/49 * 4/48 = 0.8%

you can hit a 4 of a kind with two 6s so 2/49*1/48= 0.08%

to make it short you have an EV of -0.025 coins this means you won't realise you are loosing money

sorry for my grammar but english is not my first language.