# Interesting Simulation Problems....

```Hi there, the following are some interesting simulation problems. Just
wonder how i can do it with mathematica ....

1. Problem of Points
Suppose there are two players and each player has an equal chance to
win a round.
The players agree to play 10 rounds for a pot of \$100. After player
A has won 5 rounds
and player B has won 3 rounds, they are forced by unforeseen
circumstances to stop.
how should they then fairly divide the pot? (Use Simulation to
solve)

2. Meeting Under the Clock (This problem is posed by Julian Simon(1994))

Two persons agree to arrive at the two clock sometime between 1 pm
and 2 pm and to
stay for 20 minutes. What is the probability that they will be there
at the same time?

3. Aces Probelm (Warren Weaver got this wrong in the first edition of
his book on probability)
There are four players. A bridge hand is dealt and you state to the
other three players that
you have an ace. Find the probability, as calculated by someone
else, whether or not you
also have another ace. Later, you annouce that you have the Ace of
the probability that you have another ace? (also by simulation)

4. Beagle Problem (posed by Vos Savant)
A shopkeeper says she has two new baby beagles for sale, but she
does not know whether
they are both male, both female, or a pair of male and female. You
are only interested in the
male. So she calls up the fellow who is giving them a bath and asks
if at least one of them
is a male. She then tells you that she has a male. What is the
probability taht the other one
is a male too? (simulation)

5. Bernoulli Test
Bernoulli wanted to test whether the anglesof planes of the orbits
of the known planets were randomly distributed. Modern data on the
angles of the planets wrt the ecliptic are as follows:
Mercury (7.00) , Venus (3.39), Mars (1.85), Jupiter (1.30), Saturn
(2.49), Uranus (0.77), Neptune (1.77), Pluto (17.20). Develop two test
of the null hypothesis that the planetary orbits are randomly
distributed in space. Compute p-values via resampling.

tie@cscn.com

```

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