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 =)
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Date: 2005-07-07 08:18 am (UTC)From: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