I. LOGIC

1. Two bears, one is black, one is white.

A. What is probability both are female?

B. One of the bears is female. What is probability the other
is female?

C. The bear on the left is female. What is probability the
other is

female?

Please express as a decimal, (i.e.
0.35)

ANSWER1A:

ANSWER1B:

ANSWER1C:

2. Three pancaces are in a hat. One is gold on both sides, one is
brown on

both sides,

and one is gold/brown. You pull one out, it is brown on
one side. What

is the

probability the other side is brown?

ANSWER2:

3. A hat has a coin, either black or white. A white coin is then
dropped

into the hat.

A coin is then pulled out of the hat. It is white.
What is the

probability the other

is white?

ANSWER3:

4. Given a circle. Find the probability that a chord chosen at random be

longer

than the side of an inscribed equilateral triangle.

ANSWER4:

5. Suppose you're on a game show, and you're given the choice of three

doors.

Behind one door is a car, behind the others, goats. You pick
a door, say

number 1, and the host, who knows what's behind the doors,
opens another

door, say number 3, which has a goat. He says to you,
"Do you want to

pick

door number 2?" Is it to your advantage to switch your
choice of doors

(y/n) ?

ANSWER5:

6. A town has two hospitals, one big and one small. Every day the
big

hospital delivers 1000 babies and the small hospital

delivers 100 babies. There's a 50/50 chance of male or
female on each

birth. Which hospital has a better chance of

having the same number of boys as girls (b)ig/(s)mall ?

ANSWER6:

7. You are in a game of Russian roulette, but this time the gun (a 6

shooter revolver) has three bullets in a row in

three of the chambers. The barrel is spun only once.
Each player then

points the gun at his (her) head and pulls

the trigger. If he (she) is still alive, the gun is
passed to the other

player who

then points it at his (her) own head and pulls the
trigger. The game

stops when one player dies.

Now to the point: would you rather be first or second
to shoot (1/2) ?

ANSWER7:

8. You come to a fork in a road. A person stands on each half.
One

always lies, one always tells the truth. With
just one question

find out where to go.

ANSWER8:

9. A stock price, let us call it X, follows a random walk.
Your assistant

came up with

the following strategy, which he claims will make
$1,000,000. Assume

zero transaction costs.

Let P be current stock price

Every day at 10:00, place the following limit orders:

If we have no position in X, Buy
10000 shares for P-$1.00

If we have a position in X, Sell
10000 shares for P+$1.00

At the end of each day, unifilled orders are cancelled.

Will this strategy make money?

ANSWER9A:

Why or why not?

ANSWER9B:

II. PROGRAMMING - USE PSEUDOCODE

1.

Input: arrays diff[1..n], value[1..n]

Write a program that sorts value by key in diff array (1) , then prints out

the results

in square boxes, 5 items per box ,
with data printed next to each

box like this:

**********

* 1.002 *

* 1.003 * AVG = 1.005

* 1.005 * MED = 1.005

* 1.008 *

* 1.009 *

**********

**********

* 1.012 *

* 1.013 * AVG = 1.015

* 1.015 * MED = 1.015

* 1.018 * STD = 0.011

* 1.019 *

**********

etc.

(1) Before sort diff [ 3 2 1 ] value [ 3 9 5]

After
sort diff [ 1 2 3 ] value [ 5 9 3 ] : order is

determined by the diff array

2. Write a program to simulate Logic Problem #2
1000 times, then print

the probability.

3. What does the following program output?

int rr(int x) {

int q;

static int zz;

static int zzz;

zzz++;

printf("%6d \n",zzz);

if (x<10) {

zz++;

if (zz<2) q=x/2; else q=x/3;

if (zz>1) q+=zz;

}

else {

q=rr(x-1)+rr(x/2);

}

return(q);

}

int main( int argc, char**argv) {

printf ("%d\n",rr(15));

printf ("%d\n",rr(15));

printf ("%d\n",rr(15));

}