Do you know what's worse than doing a lot of math problems? Listening to someone else talk about doing a lot of math problems. So let's suffer together, shall we?
I just spent almost an hour reviewing math problems and taking notes over topics I didn't understand or remember. These were issues I had tripped over in the previous two CLEP math practice tests. I learned a lot of symbols that I can't type in, like elements, subsets, union, intersection, conjunction, disjunction, negation, "implies", biconditional, converse, inverse and contrapositive. These are not complicated concepts, fortunately. It was just a matter of review and memorizing the symbol. I also refreshed my memory on permutations and combinations, inverse functions, Cartesian products and converting from decimal to binary and back. Overkill? I really hope so.
I then took another practice test (my third CLEP practice). Again, it was 60 questions in 90 minutes. The good news is that I only took 54 minutes to finish. I also knew a whole lot more than I did during the first test. The bad news is that I'm still rusty and made a few mistakes. I missed 9. There were 6 rusty mistakes where I understood the concept but still screwed it up. I rarely make the same mistake twice so those were what I will call "cleaning out the rust". There were only 2 that I just didn't get. And there was one that I still think I got right but they said I was wrong. I'll let you be the judge of that one:
"If you roll a pair of fair dice, the sum of the numbers on the two dice can be any number from 2 to 12. Which is more likely, getting an odd sum or an even sum?
A) An odd sum
B) An even sum
C) They are equally likely
D) None of the above"
My thinking is that there are 11 possible outcomes, like they said, 2 through 12. Of those, 6 outcomes are even and 5 are odd. Therefore you are more likely to roll an even. They said C. Correct me if I'm wrong.
3 comments:
I would have guessed C on that. The only reason is because I would have related it to that probability question where it asks if you flip a coin so many times and you get heads then are you more likely to get heads or tails and the point is you can't predict that, it's totally random.
But it seems the dice question is different, because, like your reasoning went, you should have a fixed number of roll combinations to come up with odd or even number. I thought about this, thinking, surely the test isn't wrong? And came up with the fact, if I figured it correctly, that there are 18 combinations of dice rolls that will give either an even or an odd total:
2: 1,1
4: 1,3 2,2 3,1
6: 1,5 2,4 3,3 4,2 5,1
8: 2,6 3,5 4,4 5,3 6,2
10: 4,6 5,5 6,4
12: 6,6
3: 1,2 2,1
5: 1,4 2,3 3,2 4,1
7: 1,6 2,5 3,4 4,3 5,2 6,1
9: 3,6 4,5 5,4 6,3
11: 5,6 6,5
Not sure it that's the reason it's C.. but it's interesting!
See here for the answer:
http://en.wikipedia.org/wiki/Dice#Probability
I think I get it. I wasn't thinking about it like a combination where order matters, in other words, I hadn't considered a roll of 1 and 2 separate from a 2 and 1. Thank you very much guys. I hope that ones on the test.
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