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

Home > Probability
The carnival game (Posted on 2003-09-18) Difficulty: 2 of 5
You look at a carnival game. The person running it says, "Just reach your hand into this bag. There are 9 yellow balls and 1 red ball in the bag. You get 4 chances to pull out the red ball. (You have to put the ball you drew back before you draw another ball.) You only have to pay one dollar to play, and you get 3 dollars if you pull out the red ball!"

Assuming the person running the game is telling the truth, and the balls only differ in color, would you expect to make a net profit or a net loss on this game?

See The Solution Submitted by Gamer    
Rating: 3.5556 (9 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution | Comment 2 of 30 |
(In reply to Solution by fwaff)

I would expect to lose money on this proposition, and you should, too.

I agree with fwaff's math on this, which showed that the player has a slight mathematical advantage over the house, winning an average of $0.0309 per game over the long haul. Statistically speaking, however, winning and losing comes in streaks, and for the player to win overall, she needs to bring a big enough bankroll to outlast a losing streak of potentially infinite length. Generally, players don't bring a big enough bankroll to do this, or in any case their bankroll is substantially smaller than the house's, so it is the house that has the advantage.

Sure, some players will make some dough, but most will leave a losing streak when their bankroll (or nerves) runs out, and the house should still turn a profit.
  Posted by Bryan on 2003-09-18 11:24:18

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 (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information