The only bills that aren't at least $5 are the $1 bills. There are 5 of them, so the remaining 22 are at least $5. The probability of selecting a bill that is at least $5 at random is 22/27 = .8148
2. If you are on North Carolina, your next roll could be as follows:
1/36: 2 Pennsylvania Avenue (You own, no rent or taxes)
2/36: 3 Short Line (Opponent owns, pay rent)
3/36: 4 Chance (If we were playing the actual game, we'd have to consider the probability of the different Chance card outcomes. However, the problem appears to ignore this factor, so we will treat this as a safe space.)
4/36: 5 Park Place (Opponent owns, pay rent)
5/36: 6 Luxury tax (pay tax)
6/36: 7 Boardwalk (Opponent owns, pay rent)
15/36: Greater than 7: reach Go safely
On a roll of two standard dice, the probabilities are as noted above. On the first roll, there is a 15/36 chance of reaching Go and a 2/36 + 4/36 + 5/36 + 6/36 = 17/36 chance of having to pay taxes or rent. There is also a 1/36 + 3/36 = 4/36 chance of landing on either Pennsylvania Avenue or Chance, which are safe spaces but require you to roll again before reaching Go.
If you land on Pennsylvania Avenue (1/36 chance), the possibilities for the second roll are:
1/36: 2 Chance (safe space)
2/36: 3 Park Place (Opponent owns, pay rent)
3/36: 4 Luxury tax (pay tax)
4/36: 5 Boardwalk (Opponent owns, pay rent)
26/36: Greater than 5: reach Go safely
26/36 reach go safely, 9/36 have to pay, 1/36 land on Chance and roll again.
Multiplied by the 1/36 probability of reaching Pennsylvania Avenue in the first place, and this becomes 26/1296, 9/2196, and 1/2196.
There are two ways to land on Chance: either on the first roll, or on the second roll if you landed on Pennsylvania Avenue first. The total probability of landing on Chance is 3/36 + 1/2196 = 109/1296 and the possible outcomes are:
1/36: 2 Luxury tax (pay tax)
2/36: 3 Boardwalk (Opponent owns, pay rent)
33/36: Greater than 3: reach Go safely
33/36 reach Go safely, 3/36 have to pay. Multiplied by the 109/1296 probability of landing on Chance gives 3597/46,656 and 327/46,656.
Total outcomes to reach Go safely: 15/36 + 26/1296 + 3567/46,656 = 23,973/46,656 = .5132
Total outcomes to have to pay: 17/36 + 9/1296 + 327/46,656 = 22,683/46,656 = .4862
3. You are 6 spaces away from Go To Jail, so a roll of 6 would land you there. Probability of a 6 on a pair of standard dice is 5/36 = .1389
4. Each time you try to roll doubles, you have a 6/36 = 1/6 chance of succeeding. Therefore, there is a 5/6 chance of failing.
The chances of failing three times in a row is (5/6)^3 = 125/216. Therefore, the chances that you will succeed on one of your three rows is 1 - 125/216 = 91/216 = .4213