Because we recently reorganized the material in the statistics sequence, we no longer discuss probability except as it relates to the normal distribution. Therefore I can no longer ask the following questions on my exam:
Allison claims to be a "psychic detective." She "helps" police solve crimes using her psychic "abilities." One thing she claims to be good at is providing details of where a murder victim's body can be found. Police records for 250 murders show that the frequencies with which bodies are found near trees or water areAssuming that Allison is only guessing, answer the following
questions.
1. (1 point) If Allison "sees" a body near trees and water, what is the probability that she is correct?
2. (2 points) If Allison "sees" that a body is not near trees, what is the probability that she is correct?
3. (1 point) If Allison "sees" that a body is either not near trees or not near water, what is the probability that she is correct?
4. (2 points) Allison tells the police that a murder victim will be found near water. If she is correct, and the murder victim really is near water, what is the probability that there will be trees in the area?
5. (2 points) Because Allison is only guessing, what she "sees" and where a body is found can be viewed as two independent events. Most of Allison's "visions" (.9 of them) involve both trees and water. What is the probability of the joint event that Allison "sees" a body near trees and water and the body is actually found near trees and water?
12 comments:
Fun question/scenario. Too bad probablity is not part of the course anymore. Those question are much more interesting than any of the ones I had to do when I took stats. I'll admit that probability was my least favorite part of stats but these days I wish I would have paid more attention. sigh. I was a pretty ruthless grad student, if a topic didn't interest me or address my research interests directly I generally ignored it. Very bad! Not too good for my grades either (although I always made sure to do well enough to stay in good standing)...And now prospective employers want to see my transcripts. ack.
Good luck with the exam-writing!
Liz here from I Speak of Dreams. I'm wondering why you are writing the test after teaching the class, rather than before.
Back in the neolithic when I was a TA, I found it really helpful to write the tests as a part of building the curriculum.
But maybe that's just a quirk of how my mind works.
Liz, we're on the quarter system here. I'm still teaching.
I'm so, SO sorry, AP. I feel your pain. The only thing I hate worse than making up exams is grading them. I'd almost rather take a sharp stick in the eye. The consolation is that I'm free of the office for a couple of weeks so I can catch up on my *other* teaching work.
We're on semesters here, but it still sucks. Sixteen weeks is way too long to have to go to Skool. I wish we were still on quarters...but that was long, long ago.
If it helps, having a good math teacher makes it such that even 7 years later, you still know how to solve such a problem.
Perhaps those you touched when probability was still permitted will carry the torch.
It's been years since I've taken stats, but:
1) .70
2) .18
3) .02
4) .814
5) .63
Did I pass?
I think the answer to 3) is .7 rather than .02. Simplify the logical expression. --Bob
All right except #3 - a body that is not near trees or not near water (which includes the possibility that it is not near either) occurs in (40+30+5)/250 = .30 proportion of cases.
Another way is the following: Let T be the event that the body is found near trees, and let W be the event that the body is found near water. From the table, P(T) = 205/250 = .82 and P(W) = 215/250 = .86. We want P(~T U ~W) = P(~T) + P(~W) - P(~T,~W) = .18 + .14 - 5/250 = .30.
Doh! I simplified the expression wrong. NOT A AND NOT B = NOT (A AND B) = 1 - .7 = .3
Thanks. This was fun. Perhaps you can reward us with more discarded exam questions from time to time.
--Bob
Double Doh! Still got it wrong. That should be NOT A OR NOT B = NOT (A AND B). Anyways, good problems!
--Bob
Yeah! I got them all right! I haven't had stats in years. I did like math though.
Allison sees very few bodies in the desert?
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