Assignment 6: Probability
Due at start of class on 17 February, 2006.

Name:

Each question is worth one point unless otherwise indicated.

1. You decide to play the lottery's Pick 4 game. In this game, you pick a four digit number between 0000 and 9999. If the number that you pick exactly matches the number that is randomly drawn by the lottery, you win \$5000.00. Each of the 10000 possible numbers (0000 to 9999) is equally likely to be selected by the lottery. What is the probability that you will win?
2. If it costs you \$1 to play the Pick 4 game, how much money do you expect to win each time you play? (The expected winning is given by p(WIN) * amount you win.)
3. In the long run, is it profitable for you to play the Pick 4 game? Yes No
4. The mean IQ score in the population is 100. The standard deviation is 15. What is the probability of meeting a person at random who has an IQ of 135 or above?
5. What is the probability of meeting a person at random who has an IQ of 135 or above or 70 or below?
6. What is the probability of meeting a female (from the population of both males and females) at random who has an IQ of 135 or above or 70 or below?
7. What is the probability of picking a red card from a standard deck of cards and rolling a 4 on a 6 sided die?
8. An urn contains 10 red, 10 blue, 10 green, 10 yellow, and 10 purple balls. You pick four balls at random, without replacement. What is the probability that all four balls are green?
9. An urn contains 10 red, 10 blue, 10 green, 10 yellow, and 10 purple balls. You pick four balls at random, without replacement. What is the probability that all four balls are the same color (e.g. four red balls, or four blue balls, etc.)?
10. An urn contains 10 red, 10 blue, 10 green, 10 yellow, and 10 purple balls. You pick four balls at random, without replacement. What is the probability that at least one of the balls is of a different color than the other three?
(Hint: Think about mutual exclusion and how this question relates to the previous question.)

The following two questions are bonus questions. You do not have to answer them. Each of the questions is worth 1 point. To earn the bonus points, you must have the correct answer, and you must submit your work showing how you determined the correct answer.

11. You belong to a club with 100 members. Each week (52 times a year) the club selects one member at random to receive \$10. What is the probability that you will win at least once during a given year?
12. What is the probability that you will win at least once during a two year period?