Andy, Bob, Charlie, and Dave are ready to play another round of cards. This time it is Charlie’s turn to deal.

The cards are sorted and Charlie decides to only use the Red cards (Hearts & Diamonds).

Three [3] cards are dealt one-at-a-time to each of the four [4] players. Highest pair wins; Aces are low.

If no [...]

In a test involving yes/no answers, the probability that the official answer is correct is t, the probability of getting the real correct answer is b for a boy and g for a girl. If the probability that a randomly chosen boy or girl of getting the official answer to a question is 1/2, then [...]

This problem was originally posted by Karl Sharman (with a less idiotic title).

Whilst I was away under the pretence of work, a nearby bank uncovered a plot to swap the gold in their vaults with counterfeits. It was determined that all the gold bars in three of the Bank’s seven vaults were replaced with counterfeits. [...]

Sue and Bob take turns rolling a fair 6-sided die. Once either person rolls a 6 the game is over. Sue rolls first, if she doesn’t roll a 6, Bob rolls the die, if he doesn’t roll a 6, Sue rolls again. They continue taking turns until one of them rolls a 6.

If Bob [...]

Two perfect logicians, Alice and Bob, play a game with 2n blank cards. The cards are numbered with random positive integers and laid out in a row. Alice goes first. She takes a card from either end of the row. The value of that card is added to her score. Bob then takes a card [...]

Ten perfect shooters simultaneously and independently fire at ten ducks. On average, how many ducks are killed?

(Sorry, I couldn’t resist)

I was walking through the park when I bumped into an old acquaintance.

He told me that he had two children. What is the probability that he has two girls?

A girl joined us. He said it was one of his children. What is the probability that he has two girls?

He said she was [...]

There are three fair dice, each numbered 1 through 6; one Blue, one Red, and one Yellow.

You and your opponent will each pick one die and roll. Highest number wins*.

*Special cases:

If there is a tie, and the values are EVEN: Blue beats Red, Red beats Yellow, and Yellow beats Blue.

If there is a tie, and [...]

A bag contains either a white ball or a black ball, and each case is equally likely. A white ball is added. You now randomly take a ball from the bag. If it is white, what is the probability that the remaining ball is white?

I’m not sure if this has been posted before.

Here’s a couple of picking problems.

1. If ten people randomly select their names from a hat, what is the probability that the last one will pick his own name?

2. If ten people randomly select their names from a hat, what is the probability that only the last one will pick his own name?