"Just as Mr. Summers finally left off talking and turned to the assembled villages, Mrs. Hutchinson came hurriedly along the path to the square, her sweater thrown over her shoulders, and slid into place in the back of the crowd" (266).
All right, Perrine, you're asking for it; I've whipped out math in blogs before this one, and I'm not afraid to do it again. I quote the third question. "What normal law of probability has been suspended in this story? Granting this initial implausibility, does the story proceed naturally?"
At first, I wasn't sure what Perrine was talking about, but then I had a little epiphany. Perrine wants to know what happened during the lottery that was implausible. For Perrine, I have two answers, and then I will explode on him.
First, Old Man Warner is "the oldest man in town" (5). Some people might find it odd that someone as old as Old Man Warner would have survived the lottery every year of his life and classify that as "implausible." Second, Tessie Hutchinson was the one person who showed up late to the lottery, and it just so happened that she was the . . . winner (77-79). Is that at all likely?
My first objective in this post is to determine the plausibility of these two scenarios. I'm going to make two assumptions so I can do the math: the population of this village has remained constant at 300 people during Old Man Warner's entire life, and Old Man Warner (OMW, for short) is 150 years old (a generously high age).
- The probability of OMW's survival of the lottery for his entire life is (299/300)^150, or about a 60.6% chance.
- The probability of Tessie's death as the sole latecomer is simply (1/300), or about a 0.3% chance.
- The probability of any person winning the lottery is also (1/300), or about a 0.3% chance.
Certainly, the more implausible case of the first two is the second one -- it's extremely unlikely that the sole latecomer to the lottery would be the winner. Surprisingly, it's somewhat likely that someone can live to be 150 years old without winning the lottery in the village.
My second objective in this post is to say this very clearly. NO NORMAL LAW OF PROBABILITY HAS BEEN SUSPENDED, AND YOUR SENTENCE USES PASSIVE VOICE. I feel very strongly about this. Just because it was unlikely that Tessie (the only person who came late) would be stoned does not mean that a law of probability was suspended. The laws of probability always stand, even when the most likely outcome does not occur.
Unless someone can convince me that Perrine was referring to some other rule of probability, I will remain angry at him. Perrine, you stick to literature, and I'll stick to math, and we won't have to cross each other anymore once I finish this class.
Your math is wrong statistically speaking Bryan. See, not everyone has a likely chance of being picked in the lottery. Since Mrs. Hutchinson comes from a family of 5, she has a 20% chance of being picked should her family come up, whereas OMW has no known family I believe, so he has a 100% chance of being picked should he draw. In this scenario, we'll have to assume a set number of family, let's go with 50 for easier math (6 people per household seems plausible when in this setting). In this case scenario the chance for OMW to be picked is simply (1/50)*(1.00) leaving him a 2% chance of being picked.
ReplyDelete"Seventy-seventh year I been in the lottery," Old Man Warner said as he went through the crowd. "Seventy-seventh time."
Now since he has a 2% chance of being picked every year (assuming a stable 300 people in the village). We can take (.98)^(78) to get a 20.684% chance of him never being picked to this point. To confirm my math we can use a geometric distribution to find the chance that he would have been picked on or before his 78th pick. 1-Geometcdf(0.02,78) which gives us a 20.684.
So now we have to compare this with the probability that the last person to arrive gets chosen. This number is constantly changing, but we can find the probability that Mrs. Hutchinson is chosen on this particular day. To do this, we can just use a similar process to OMW. Since she has a five member family, her chance to be chosen is 20% should her family be chosen, which will happen 2% of the time assuming the slips of paper are fair. So, Mrs. Hutchinson has a [(0.20)(0.02)] or 0.40% chance of being chosen today.
This, my friend, is the suspended law of probability. In a normal probability, everyone would have the same chance of being chosen, but because of the multilayer style of this lottery, not everyone has the same chance of being chosen.
Bryan, you stick to Physics, and I'll stick to Statistics, and we won't have to cross each other anymore once we finish Calculus.
My post was funny, but now you're just being difficult.
ReplyDeleteThe only concession I will make is that Old Man Warner has participated in 77 lotteries, a number I couldn't find when I was collecting data. Take my math to mean that even after 73 more lotteries, Old Man Warner still has a significant chance of surviving.
However, there's a problem with suspended probability in the case of this story -- the reader doesn't know how many families there are in the village, and the reader doesn't know how many family members Old Man Warner has. Certainly, he hasn't lived his entire life without any family.
Therefore, rather than assuming that there are 50 families and that Old Man Warner lives alone, I assumed that all of the families were equal in size, an assumption less random than yours. You could have just as easily said that there were 60 (not 50) families and Old Man Warner lives with 4 (not 0) other people, which would have confirmed my math perfectly, but you didn't simply because your primary purpose was to disprove my own math.
With my assumption in place, each person has an equally likely chance of being chosen in the lottery. While we know of villagers with no families and can imagine villagers with huge families, that assumption isn't terribly far off -- I simply chose to base my family average on Mrs. Hutchinson's family, a levelheaded decision on my part.
Here, we see the issue of trying to quantify literature. There are many ways to do it, and there are many discrepancies along the way. It's quite tragic.
I'm not saying in this comment that your math is wrong and mine is right. All that happened is we made different assumptions in our calculations, so I don't think it fair for you to insult my probability skills. There's an infinite amount of ways for us to calculate probabilities within the story.
What's important is that we both came up with relatively close numbers that suggest that (a) Old Man Warner is likely to have survived the lottery his entire life and (b) the last person to show up to the lottery has a tiny chance of being selected. All together, (c) no laws of probability were suspended in the story. If you'll agree with those three points, I would be glad to accept a truce.
..I can't believe you took the time to do all that math =o
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