Browse Teasers
Search Teasers

Balls in a Jar

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #26847 Fun: (2.46) Difficulty: (2.17) Category: Probability Submitted By: shenqiang Corrected By: Dave

You're walking down a street, when you see some people gambling on the roadside.

The dealer says:

"There are 10 black balls and 10 white balls in this jar. You are blindfolded and you randomly pick 10 balls. If 5 of the balls you picked are black and the other 5 are white, you lose \$2. Otherwise you win \$1."

Is the gamble fair?

The number of combinations to take 10 balls out of 20 is 20!/(10!)^2=184756.

The number of combinations to take 5 balls of each color is (10!/(5!)^2)^2=63504.

This means in 184756 games you lose 63504 games and win 121252 games in average, totaling a loss of \$5756. In other words, you lose about \$0.03116 per game in average.

Therefore, the gamble is not fair.

Hide

What Next?

See another brain teaser just like this one...

Or, just get a random brain teaser

If you become a registered user you can vote on this brain teaser, keep track of
which ones you have seen, and even make your own.