Carnival Question

A clerk in the butcher shop is 5' 10'' tall. What does he weigh?

Locked Drawers and Lost Files

A man working in a cube has 10 drawers in which to store his files. Two of the drawers can be locked. Each time he stores a file, he picks one of the drawers at random and places it inside.

Yesterday he locked the two drawers that could be locked, but when he came in this morning, he realized he had forgotten his keys at home. He realizes he needs one of his files and begins to look for it. His search is simple, picking each drawer in order, he rifles through each one until he finds the file he needs. He does not go back to any drawer he has already checked.

1) He checks the first drawer, but doesn't find the file. What are the chances he finds the file in the remaining 7 drawers? (Remember, he can't check the last two!)

2) He checks the first four drawers and has not found it. What are the chances he will find the file in the remaining 4 drawers he can open?

3) He has looked in the first seven drawers. What are the chances he can find the document in the final drawer?

Probability of Bears

There are two bears - white and dark.

1. What is the probability that both bears are male?

If we write m for male and f for female, we have four possibilites: (mf, fm, mm, ff) which means the probability of mm = 1/4 (assuming they are all equally possible).

2. What if I told you one of the bears is male? What is the probability they are both males?

The possible outcomes are (mf, fm, mm), which means the probability they are both males is 1/3.

3. Now, what if I told you that the lighter bear is known to be male. What is the probability they are both males?

Truth, Lies, and Islands

The inhabitants of an island tell truth one third of the time. They lie with the probability of 2/3.

On an occasion, after one of them made a statement, another fellow stepped forward and declared the statement true.

What is the probability that it was indeed true?

Envelope, Please

In a box there are two envelopes. It is known that with probability 1/2, one envelope contains $1 and the other one $10; with probability 1/4, one envelope contains $10 and the other one $100; with probability 1/8, one envelope contains $100 and the other one $1000; and so on.

You open one envelope and find x dollars in it. Now you can keep the money or take instead the other envelope. What do you do?

Flawed Nobel Prize

On the occasion of his receiving second Nobel prize, Dr. Linus Pauling, the chemist, remarked that, while the chances of any person in the world receiving his first Nobel prize were one in several billion (the population of the world), the chances of receiving the second Nobel prize were one in several hundred (the total number of living people who had received the prize in the past) and that therefore it was less remarkable to receive one's second prize than one's first.

What is the flaw in Professor Pauling's joke?

Sold Out Flight

On a sold out flight, 100 people line up to board the plane. The first passenger in the line has lost his boarding pass, but was allowed in, regardless. He takes a random seat. Each subsequent passenger takes his or her assigned seat if available, or a random unoccupied seat, otherwise. What is the probability that the last passenger to board the plane finds his seat unoccupied?