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

[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*