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Thoughts, opinions? Am I a huge meanie or what? It's review for their midterm on Wednesday, so at least it will not be time wasted =) =) Is it too easy?
Review Problems
July 1, 2005
1. You are living in a time before the Internet (sometime just after the Commodore 64 came out), somewhere in the 213 area code (Los Angeles). Your parents just bought you a Commodore 64 computer (YIPPY!), and you have just found out about BBS boards from a friend in high school. You wish to find more BBS boards and other computer systems online, so you program a war dialer.
(a) If your war dialer can go through and try 15 phone numbers a minute, potentially how long will it take to check every phone number in the 213 area code?
(b) You score a hit with one of your phone numbers and it turns out to be a computer for the Department of Defense. The computer is password protected, however. It is six digits long, composed of numbers and letters. You write another program which cracks passwords. How many passwords might your cracker potentially have to go through before it finds the correct one (assuming repetitions are allowed).
(c) How many assuming repetitions are not allowed?
Note: (excerpt from The New Hacker's Dictionary):
war dialer /n./
A cracking tool, a program that calls a given list or range of phone numbers and records those which answer with handshake tones (and so might be entry points to computer or telecommunications systems). Some of these programs have become quite sophisticated, and can now detect modem, fax, or PBX tones and log each one separately. The war dialer is one of the most important tools in the phreaker's kit. These programs evolved from early demon dialers.
2. A card is drawn at random from a deck of 52 cards? What is the probability that the card is a jack given that it is a face card?
3. What is the probability of winning the Washington State Lotto? You must pick 6 numbers (1-49).
4. The payoffs for betting $1.00 in the Washington State Lotto are as follows:
match 6 of 6 win 1,000,000
match 5 of 6 win $1,000
match 4 of 6 win $30
match 3 of 6 win $3
The actual jackpots may be higher depending on who won the previous week. But they all start at a minimum of 1,000,000. Obviously, if you match less than 3, you lose your $1.00 and don't win anything. Also, let's assume that the state keeps your $1.00 bet regardless of what the payoff is.
(a) What is E($1.00 bet)? That is, what is the expected payoff for a $1.00 bet? Use this number to calculate the house edge (in this case the house is the state of Washington)?
(b) If 500,000 people on average buy 2 Lotto tickets a month, how much money does the state of Washington take in in revenue per month from Lotto?
5. What is the probability that the sum of two rolled dice is 10 given that at least one of the rolled dice is a 2?
6. About 10% of all men are left-handed and about 8% of all women are left-handed. Approximately 49% of the US population are men, and 51% are women. What is the probability that a randomly selected person in the United States is a left-hander?
7. There are 10 people in a room. What is the probability that at least 2 of them were born in the same month?
8. You have a horrible fear of flying. You are taking a flight from Denver's Stapleton Airport to Rapid City, South Dakota. The plane you are boarding has twin engines - each of which has a failure rate of .00001%. What is the probability that both engines will fail during the flight? Assume the failures of the two engines are independent of each other.
Review Problems
July 1, 2005
1. You are living in a time before the Internet (sometime just after the Commodore 64 came out), somewhere in the 213 area code (Los Angeles). Your parents just bought you a Commodore 64 computer (YIPPY!), and you have just found out about BBS boards from a friend in high school. You wish to find more BBS boards and other computer systems online, so you program a war dialer.
(a) If your war dialer can go through and try 15 phone numbers a minute, potentially how long will it take to check every phone number in the 213 area code?
(b) You score a hit with one of your phone numbers and it turns out to be a computer for the Department of Defense. The computer is password protected, however. It is six digits long, composed of numbers and letters. You write another program which cracks passwords. How many passwords might your cracker potentially have to go through before it finds the correct one (assuming repetitions are allowed).
(c) How many assuming repetitions are not allowed?
Note: (excerpt from The New Hacker's Dictionary):
war dialer /n./
A cracking tool, a program that calls a given list or range of phone numbers and records those which answer with handshake tones (and so might be entry points to computer or telecommunications systems). Some of these programs have become quite sophisticated, and can now detect modem, fax, or PBX tones and log each one separately. The war dialer is one of the most important tools in the phreaker's kit. These programs evolved from early demon dialers.
2. A card is drawn at random from a deck of 52 cards? What is the probability that the card is a jack given that it is a face card?
3. What is the probability of winning the Washington State Lotto? You must pick 6 numbers (1-49).
4. The payoffs for betting $1.00 in the Washington State Lotto are as follows:
match 6 of 6 win 1,000,000
match 5 of 6 win $1,000
match 4 of 6 win $30
match 3 of 6 win $3
The actual jackpots may be higher depending on who won the previous week. But they all start at a minimum of 1,000,000. Obviously, if you match less than 3, you lose your $1.00 and don't win anything. Also, let's assume that the state keeps your $1.00 bet regardless of what the payoff is.
(a) What is E($1.00 bet)? That is, what is the expected payoff for a $1.00 bet? Use this number to calculate the house edge (in this case the house is the state of Washington)?
(b) If 500,000 people on average buy 2 Lotto tickets a month, how much money does the state of Washington take in in revenue per month from Lotto?
5. What is the probability that the sum of two rolled dice is 10 given that at least one of the rolled dice is a 2?
6. About 10% of all men are left-handed and about 8% of all women are left-handed. Approximately 49% of the US population are men, and 51% are women. What is the probability that a randomly selected person in the United States is a left-hander?
7. There are 10 people in a room. What is the probability that at least 2 of them were born in the same month?
8. You have a horrible fear of flying. You are taking a flight from Denver's Stapleton Airport to Rapid City, South Dakota. The plane you are boarding has twin engines - each of which has a failure rate of .00001%. What is the probability that both engines will fail during the flight? Assume the failures of the two engines are independent of each other.
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no subject
Date: 2005-07-01 07:26 pm (UTC)From:Hmm...this is a toughy...I really suck at stuff like this because I'm in the total minority when it comes to college students.
I don't think you're a meanie at all. However, you know some of your students are going to be burning your name in effigy. So, it won't make you popular, but it won't kill them, either.
As for the questions: hee! They're so awesomely worded! I wanna take your class. *whine* I don't think it's too easy. It sounds fairly typical of the probability stuff I went through. Your questions offer a wide variety of situations and ask the students to test indepent probabilities (why no, no i don't recall any math lingo *grin*).
~e!
no subject
Date: 2005-07-01 07:58 pm (UTC)From:Anyway...glad you like the questions! I strive to be creative =)
no subject
Date: 2005-07-01 08:00 pm (UTC)From:Again with the me not being normal, tho' ;)
You're very creative. It sounds like such a fun test!
~e!