Will they meet?

Two friends arranged to meet at a railway station, but they'd arrive between 1pm and 2pm, would wait for up to 15 minutes and leave if the other didn't turn up during that time. What is the probability that they actually meet?

NB if they meet, it must be between 1pm and 2pm.

Reducing random numbers

Pick a uniformly distributed random number between 0 and 1. Continue picking until you pick one that is larger than the previous one that you picked. What is the expected number of numbers you pick (including the one that ended the sequence)?

NB Expected means average.

Queue height

Some (n) people are standing in a queue. On average, how many of them can say that they are taller than everyone ahead of them?

NB The person at the front of the queue, can say that he is taller than everyone ahead of him.

How many sons

I. Mrs. Jones has two children. At least one is a boy. What are the chances that both are boys?
II. Mrs. Brown has two children. The younger one is a boy. What are the chances that both are boys?

Free gifts

A breakfast cereal includes a free gift is included in each box. There are six different gifts. Assuming there is an equal chance of getting any one of the gifts, what is the expected number of boxes you need to buy in order to get all six gifts?

Average number

If the probability of an event happening in one trial is p, the average number of trials needed to get the event is 1/p. Why is that true?

Three bags of marbles

You have three bags of marbles. The first bag contains two white marbles, the second contains two black marbles and the third contains one black and one white marble.

You pick a bag at random and take out a marble. It is white. What is the probability that the remaining marble in that bag is white?

Odd Streak of Heads

On average, how many times do you need to flip a fair coin before you have seen a run of an odd number of heads, followed by a tail?

The Gambler's Ruin

At the beginning of play, gamblers A and B have m and n chips, respectively. Let their probabilities of winning be p for A, and q=1-p for B. After each play, the winner gets a chip from the loser, and play continues until one of the players is ruined.

What is the probability of A being ruined?

Chess Squares

What is the probability to randomly chose any 3 squares on a chess board, and they would form a continuous diagonal?

You don't hold a chess board in your hands to solve this one. simply think.

Deer Dilemma

In Kisatchie National Forest in Louisiana, where there are thousands of deer, one out of 10 on an average is a blackbuck (endangered species). If you happen to shoot at random 10 deer in this forest, what is the chance that you will have hit at least one blackbuck? And how many deer do you need to shoot to be sure with a confidence of 90 percent that a blackbuck has been shot?

700 MB CD

I have a file to put on a 700 MB CD.

Windows explorer says the file size is 717,112 KB.
So I expect it's not going to fit.
What's the probability that it WILL fit?

If so, why?

(Boy are things going downhill. I think everyone burned out their brains on the 720!)

dicey die

By mistake, two dice have been made with the four side replaced with a copy of another side. It is the same error for both dice. Because of the error, the probability of throwing seven is 1/3 less than usual. What has the four side been replaced with?

flipping furniture

Whilst doing experimental probabilty, Ragknot ended up with ten coins under his couch. He decided it was now worth the effort to retrieve his accrued fortune. Amazingly the first nine coins he found were heads up. What is the probability the last one will be heads up as well?

Clarification - As I might have outsmarted myself, I want the problem to be interpreted as:
If you flip 10 coins and at least 9 of them land heads up, what is the probability that all 10 will be heads up?

More marbles

You have two identical looking bags. One bag has three black marbles and one white marble. The other has three white marbles and one black marble. After choosing a bag at random, you draw one marble from it at random. It is black. You then put it back in the bag and then draw another marble from the same bag at random. What is the probability that the second marble is black?

As there have been quite a few probability problems lately, I'll not post another for a while - unless it's excellent.

What a shot!

A young man stands on the top tier in a football stadium
(no, not soccer). He throws a basketball to the football field
below (let's assume it's 500 feet horizontal and 50 foot lower)
to a bastetball goal, and makes it. What was the probability of
making this basket?

Assuming that he has tried many, many times, and 85%
of the time he can come within a 20 foot radius of the
center of goal.

You can see this video at http://RagKnot.blogspot.com

(Texas A&M University is where I went to school.)

To save time: diameter of goal 17 inches. diameter of ball 9 inches.
The shot was what we call a bank shot, not a "net only".
(An only net would be harder to make)

Sick or not?

10% of people have a particular disease. A test for the disease gives the correct result 90% of the time (i.e that they do or do not have the disease). If a person is picked at random and the test result is positive, what is the probability that that person has the disease?