Check out the midterm my students are taking tomorrow...

[gray_ghost]

1. Suppose a couple has two children. Find the probability that both children are boys if it is known that:
(a) At least one of the children is a boy
(b) The older child is a boy

Hint: The space of all possible outcomes is S = { bb,bg,gb,gg }

2. Suppose a student dormitory consists of:
60% first-year students (10% of whom own a car)
40% second-year students (20% of whom own a car)
Find the probability that a randomly selected student in the dormitory owns a car.

3. The Pentagon computer which you hacked into in the last homework assignment has become self-aware, and has come to the conclusion that human beings are a lower form of life which must be eradicated. To this end, it is attempting to guess the nuclear launch codes for all the nuclear missiles in the US nuclear arsenal (over which it has omniscient control).

The launch codes are of the form: XXX-XXX-XXX
The first block can be any combination of letters or digits.
The last two blocks must be numbers.

If the computer can try 2,000,000 codes a minute, how many minutes will it take before all possible codes have been tried?

4. If one card is drawn from a deck of 52 playing cards, what is the probability that you do NOT draw a face card or a heart?

5. In South Dakota Hot Lotto, 5 balls are drawn from one drum (the balls are 1-39), and a Hot Ball is chosen from a second orange drum (Hot Balls are numbered 1-19). What is the probability of picking all 5 numbers + Hotball?

6. Write down your first name. How many different permutations in the letters of your name are there?

7. If a coin is flipped 12 times, what is the probability that you get exactly 4 heads?

8. What is the probability that the sum of two rolled six-sided dice (numbered 1-6) is 10 or greater given that at least one of the rolled dice is a 5?




I just realized something. I am totally going to have to flock my journal in the future if I continue to teach. It is way too dangerous to have an open blog out there with a bunch of students who are probably online all the time, googling for their professor because they are bored and curious. *sigh*

Well for now - just this entry.

Comments

[phendog.livejournal.com]

1) bb, bg = .5
2)=0.4*(0.2)+0.6*(0.1)= .14
3) =(36*36*36*10^6)/2000000=23328 minutes (assuming the computer doesn't find the answer before that and quit looking!)
4) 30/52 or 0.5769
5) =1/39*1/38*1/37*1/36*1/35*1/19 = 7.6^-10
6) *is embarrassed to admit that I don't really understand this question, but I'll try* AMBER = 5!, = 120 combinations of letters?
7) Ugh. I don't remember the formula for this, and I'm WAY too lazy to figure it out longhand. So I'm going to take the loser way out and say 4/12 = 0.33 for partial credit?
8) 2/6 = .33


So...how did I do? Honestly, I hated that class...hence why I can't remember most of the more advanced formulas.

[katekat]

I want to know how she did too! It looks like greek to me!

[phendog.livejournal.com]

4) (assumes the only face cards are K, Q, J)

7) Still bothering me...okay, you're going to think I'm completely nuts, but...I did it long hand. Assuming I didn't screw up, there are exactly 495 possible combinations. Assuming each has a probability of .5^12 then: =495*.5^12 = 0.12 Did I screw up, or is that right?

(You can see the excel file if you really want w/all the combos *hee*)

[gray-ghost.livejournal.com]

You got 1(b) right. If the older child is a boy, then your space of outcomes is reduced to {bb,gb}. Therefore, there is 1/2 probability both children will be boys.
1(a) is 1/3 (because the space of outcomes is {bb,bg,gb} so there is 1/3 probability both kids will be boys.

2. yup! correct!
3. correct
4. correct
5. nope....there are 39 choose 5 ways to pick the first 5 correct balls (39!/5!34!) and 19 ways to pick the Hotball. Since there is only one way to pick all 6 numbers:

p(win) = 1/(39 choose 5)*19 = 1/10930383 = .000000091 blah blah blah anyway....odds of winning are next to zilch.

Incidentally - this is real example. I went to website for South Dakota lottery to get it. I already worked out the probability of winning Washington's Lotto (which is about the same).

6. correct (and hey I didn't know that was your real name...I've gotten so used to thinking of you as phen or phendog. Amber is pretty =) )

7. correct (your second answer, not your first) And you are nuts...that's not up for debate =)
8. correct!

okay - so you missed one problem (which was worth 6 points (I'll give you 2 partial credit points for writing something down), and half of the first problem (-3 points). So your score on this midterm would have been 43/50 = 0.86 = 86%

With the curve that is going to exist in my class, I think that might be an A =)

--tyler

[phendog.livejournal.com]

Woot!

And I'll challenge the first question because I didn't realize that was a two parter (a) and (b). I thought (a) and (b) were conditions for one question! I did wonder though that the one seemed to make the other a moot point...

Yeah, no way I would have gotten 5...and honestly, 7 probably shouldn't count because there's no way I would have had time for that during a test! What's the easy formula?

6) Thanks. I don't give out my real name hardly ever on-line just because. Though I keep telling my parents it's a stripper name *LOL*

[glimmergirl.livejournal.com]

*skips the mathy bit because it's been WAY too long since I understand even parts of stuff like that*

:)

I try to keep the public parts of my journal as non-identifiable as possible, and right now pretty much only my writing, graphics and a meme every now and then is in a non-locked post. While I don't think any of my past or future students would be able to find me, you never know. It's just easier to not have to worry about losing your privacy.

[katekat]

y'know, I didn't even think about that - I guess I'm used to the idea that you actually can't find people you're looking for in cyberspace, unless you know where to look...

Do you have any personal identifiers in your User Info? Especially stuff that students might know? I thought you only used/mentioned your university contact info to them. It's not like your handle's "This is the LJ of Tyler Wilson" or anything....

[gray-ghost.livejournal.com]

Students can get very creative about ways in which they find people. You don't have to do it strictly through the user info. You can Google text as well. Also - you can search LJ by location. I could lie and change my location to what it used to be (Fullerton).

Anyway...it's a little tiresome trying to keep track of things I should or shouldn't say in an open blog because someone might google that particular phrase.

Of course my user id is completely ungoogleable (benefit of picking nickname of a famous dead civil war general).

[katekat]

All I have to say is that you found Ian McDonald and you *didn't tell me*!?!?

Bastard.

But yeah, you'd be hard to find, I think. But I am not a crafty undergraduate with too much time on my hands. And I'm sure most of 'em have paid LJ's so they can search the location info. Sigh. You could opt not to display that (I think it's an option) or just choose Canada, since you're going to go there someday anyway.

[phendog.livejournal.com]

You can definitely opt not to fill in location. I never did.

[gray-ghost.livejournal.com]

Oh yeah...sorry. He was getting into a flamewar with a bunch of the hard SF types (which are loved so much on Slashdot), and giving them hell. So I found his link through there.

[phendog.livejournal.com]

*nod, nod* Amazing what students can find indeed.

We had a prof once that claimed to be an original mouseketeer (on the show!). There was a mouseketeer with the same name...so we found out who that mouseketeer was, what he looked like, and where he lived now. Definitely not our prof. So we thought maybe he did it under another name and researched each one. Finally we found of the original mouseketeers to contact and asked him personally whether he knew our prof or thought he might have ever been one of the mouseketeers. He (Lenny?) said no, he had no idea who our prof was and he definitely had NOT been an original mouseketeer. Suffice to say, we caught our prof in a lie that got him in quite a bit of trouble (since he'd even told admin the story).

But yeah...googling text is easy. And I HAVE been known to google tests (because if a prof takes a test off a site, chances are future tests might come from that site as well...*shh!* Don't tell anyone I know that!)

[gray-ghost.livejournal.com]

Why would you lie about being a mouseketeer? *L* I can see lying about a lot of things...but sitting alongside Annette Funniccello belting out nationalistic ballads for Der Fuhrer MausLand is not one of them.

I love Disney though! I really do! If anyone asks, tell them I really REALLY love Disney.

I really love how you can Google the text inside PDF docs and other file formats (since especially with PDF, it's so popular among academic types).

Oh - hours of fun if you're interested: [Google Hacks] (http://douweosinga.com/projects/googlehacks)

Do kind of wish there was an alternative to google which was just as good. No one comes even close though. It's scary though how powerful they are becoming as a force online.