alecks wrote:
Section 2 #8: I had trouble with this question because I didn't see the flaw, and still don't. Can you explain how A is correct?
Statistics!
Alright, that's probably scarier than the question.
My conclusion here is that this critic is exaggerating the risk - in other words, there's a smaller risk than he's stating.
Why is this the case?
Because a fatal catastrophe is unlikely at each stage of the trip.
In short, the author is saying that each step is pretty safe, so the trip overall is pretty safe.
Well, even without the statistics lesson I'm about to give, what's going on here is a composition fallacy - just because a part of something has a quality, it doesn't mean the whole thing has that quality. Here, just because each step is unlikely to see catastrophic failure doesn't mean that the trip as a whole won't see catastrophic failure.
Why? Because let's say that the chance of each step failing is 1%. So you'll survive that step 99% of the time.
Well, add a second step on - the chance of surviving is now 98.1% (.99*.99) - still pretty good. But what if there are 100 steps, each with a 1% chance of failure? In that case, you only have an ~37% chance of survival. But we know the trip to Mars is long and complicated, so it might be 1000 steps - in which case, your chance of survival is .0000432% - never tell me the odds!
In short, small risks can add up over time to create a large risk. If you were to roll a die with 100 sides and get killed on a 1, would you feel safe rolling it once? Maybe. But each time you roll it, you're statistically a little closer to your number coming up.
Section 2 #21: I had trouble diagramming this one.
Large nurseries --m--> Sell Raspberries primarily to commercial growers
Large nurseries --m--> Sell only healthy plants (It's got Paul Anka's guarantee*)
(since it's an "and" statement in the necessary condition, I can break it up; and you should, because it's easier to deal with. Rules: an "or" in the sufficient can be split; an "and" in the necessary can be split)
Johnson's shipment: Not healthy and From Wally's Plants
A - we don't know anything if Wally's isn't a large nursery
B - we don't know the size of Wally's nursery
C - we can't draw a conclusion about things not being a large nursery (because it only shows up as a sufficient condition, and I can't take the contrapositive of a "most" statement)
D - well-run? Where'd that come from? Also, this is saying it's not a large nursery which, again, we can't conclude.
E - Bingo. If it's a large nursery, then it is likely to sell primarily to commercial growers and have a disease-free guarantee. Since the raspberries it sent to Johnson's were riddled with disease, then it is likely that it broke the guarantee.
*Void in Tennessee.
. She's going to be around the forum, posting replies to threads and holding office hours here. For now, she's going to be in this thread on Friday afternoons (I'll still be around Wednesday nights), but we'll be expanding that in the future so that we'll have even more times when you can get a quick response to a question.
