Having trouble grasping these concepts. Any help would be greatly appreciated.

1) You are rolling a pair of 6 sided dice. Find the probabilities.

i) sum is greater than 5 on two rolls in a row.........i got the answer 13/18

j) sum is greater than 5 on either 1st or 2nd throw........i got the answer 169/324

2) Using a standard deck of 52 cards compute the following probabilities

a) at least 1 black card in a 5 card hand.....i got 65780

b) at least 1 face card in a 5 card hand.......i got 792

c) a flush in a 5 card hand.....i got 1287

d) a flush in a 7 card hand......i got 1716

3) from a standard deck of 52 cards, 1 card is drawn

a) find P(diamond|red). are these two independent? ........i got 1/4, dependent

b) find P(even|diamond) (assume face cards no value) are they independent......i got 1/8 independent

c) if you are playing a game where you win 100$ if your card is king. If the game is fair, how much should you loose if you do not draw a king?....i got $8.33

4) you flip 2 coins. you win $2 if the coins show the same side and you loose $3 if they show different sides. what is the expected value of this game. how much should you loose for the game to be fair?......i got $2

5) 5000 raffle tickets are sold at $1 for a charity raffle. The prizes being offered are: 1 prize of $500, 3 prizes o $100, 5 prizes of $20, and 20 prizes of$5. Construct a payout table. Calculate the expected value for purchasing one ticket.........i got -$0.82 per ticket

6) one of two urns is chosen at random with one as likely to be chosen as the other. Then a ball is withdrawn from the chosen urn. Urn 1 has 1 white and 4 red balls, and urn 2 has 3 white and 2 red balls.

a) if a white ball is drawn, what is the probability that it came from urn 1...i got 1/4

b) if a white ball is drawn, what is the probability that it came from urn 2...i got 3/4

c) if a red ball is drawn, what is the probability that it came from urn 1....i got 2/3

d) if a red ball is draw, what is the probability that it came form urn 2....i got 1/3

7.) Find the probability that a randomly chosen positive integer less than or equal to 1000 is divisible by 6 or 8...i got 1/4