ManishKM1 wrote:
Hi mikemcgarry,
Can we actually take the likelihood as a fact in reaching to the conclusion? Like mentioned in the argument, "recidivism rate for the convicts that Judge Brown has apologize has dropped to 15%, down from the standard 35%." is not a fact but an approximation. Can you pls help?
Regards
Dear
ManishKM1,
I'm happy to respond.
My friend, the human sciences are messy, especially when compared to the natural sciences. There's a high level of precision in the natural sciences--every time we mix the same two chemicals, the same thing happens, like clockwork. Computers and coding also have that level of precision: the same line of code will do the same thing each time. Real human beings are messier than computers or lab chemicals. Real human beings are idiosyncratic, unpredictable, and unreliable. Real human beings often behave according to trends, but regularly act completely counter to expectation.
My friend, I don't know what you studied in your undergraduate degree, but if it was anything in science or engineering or computers, it may be that you need to familiarize yourself with the "feel" of social sciences--psychology, sociology, anthropology, etc.
The prompt says:
He [Judge Brown] argues that the rate of recidivism, or the likelihood that the criminal will commit another offense, is only 15% when he does so, while the average rate of recidivism in the country as a whole is above 35%. To a math or computer person, those look like probabilities. To someone who has studied the social sciences, a drop from 35% to 15% is mind-bogglingly good! If a social scientist got such a large different in her own results, she would dance for joy! This is an enormous difference. If that's not apparent to you, you have to get yourself more familiar with some of the social sciences.
Also, purely on mathematical grounds, keep in mind
what probability really means. Let's talk about a fair coin. When we say that the probability of H is 1/2, we are making a precise mathematical statement, not an approximation. We are saying that any individual flip of the coin is random, unpredictable, and even a small number of flips in a row would be relatively unpredictable, but if we were to flip that coin a large number of times--100, 1000, 10000, etc.--then we necessarily would see a pattern of very close to 50% H and 50% T. I don't know whether you understand the calculus idea of a limit, but the limit as the number of trials goes to infinity is equal to the probability. That large-scale statement is not an approximation at all! Mathematically, probability is always a statement of complete uncertainty in the individual instance and of 100% certainty in the long-run overall pattern. Flip a coin once, and I have no idea how it will turn out. Flip a coin 10,000 times, and I can make a precise prediction about the narrow range of outcomes.
Of course, real human beings are not as neat and precise as coins, but similar principles apply. The 35% and 15% are statements about the overall pattern, about the long-term trend in the data. These numbers doesn't allow us to know much of anything about how one individual in isolation might behave, but they tell us deeply meaningful information about the large-scale population pattern. Once again, the population-wide statement is NOT an approximation: instead, it is a meaningful quantitative statement about an overall proportion of a relevant population.
I am going to recommend this blog to you:
GMAT Critical Reasoning and Outside KnowledgeDoes all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)