All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Games
The Dice Game (Posted on 2005-11-04) Difficulty: 2 of 5
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.)

See The Solution Submitted by Gamer    
Rating: 3.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
MY SOLUTION | Comment 5 of 12 |

The optimum strategy would be to guess "higher" on rolling a 1, 2, or 3 and "lower" on a 4, 5, or 6.

probability formula for an event is

number of favourable outcomes / total numer of events

so for each roll of the dice while adhering to the optimum strategy there are 28 favourable outcomes out of a total outcomes of 36.

so plugging these values into the formula we have 28/36 or 7/9

now given that each roll is an indepentant event we use the multiplication law for independant events.

so for the overall probability we multiply the independant probabilities by each other and we get 7/9x7/9x7/9x7/9

this equals   2401/6561 or 36.6% chance of a favourable outcome.


  Posted by Leigh Lillico on 2005-11-06 04:05:41
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information