In a game show, there is a certain game in which there are four hidden digits. There are no numbers greater than six among them, and no zeros.
You roll a die and then guess if the first digit is higher or lower than what you rolled. (If the die you rolled is equal to the first digit, you win no matter what you said.) You then roll and guess for each of the other three digits.
If you use the best strategy each time when saying "higher" or "lower", what is the chance you will get all four right and win? (Keep in mind you have no idea what the 4 digit number is.)
If you roll a 1 you guess "higher"
If you roll a 2 you guess "higher"
If you roll a 3 you guess "higher"
If you roll a 4 you guess "lower"
If you roll a 5 you guess "lower"
If you roll a 6 you guess "lower"
If you roll a 1 you have a 6 in 6 shot in the right number
If you roll a 2 you have a 5 in 6 shot in the right number
If you roll a 3 you have a 4 in 6 shot in the right number
If you roll a 4 you have a 4 in 6 shot in the right number
If you roll a 5 you have a 5 in 6 shot in the right number
If you roll a 6 you have a 6 in 6 shot in the right number
You have a 30 in 36 shot in the right number for each number
You have a 120 in 144 shot in the right number for each number
120/144 = .833 which is a 83% chance of guessing the right number and winning.

Posted by Heather
on 20051110 23:41:44 