What normal law of probability has been suspended in the story "The Lottery"?

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In Shirley Jackson's "The Lottery," the law of probability that has apparently been suspended is the one that should apply to Old Man Warner.

As the townspeople stand only half-listening to the directions of Mr. Summers, who is in charge, some of them begin to gossip among themselves. Soon, the family names are called and the heads of the family reach into the box pulling out a small folded paper. As this procedure continues, Mr. Adams tells Old Man Warner that the residents of the north village have decided to be rid of the lottery. The older man snorts in disgust:

"Pack of crazy fools....Listening to the young folks, nothing's good enough for them....There's always been a lottery....Bad enough to see young Joe Summers up there joking with everybody."

The curmudgeon Old Man Warner continues to argue there is "Nothing but trouble in that." Then, when Mr. Warner is called to the front, he squeezes through the crowd, saying, "Seventy-seventh year I been in the lottery.....Seventy-seventh." This fact certainly contradicts the law of probability, given the small number in the population of the village.

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Is your question refering to the way in which the lottery is done in specific stages? If we have a look at the story, the way that a member of the village is selected is done in two different stages. Firstly, a family is selected, and then secondly a member of that family is selected to "win" the lottery. Consider what we are told by Mr. Summers as he explains the first stage of the lottery:

Now, I'll read the names--heads of families first--and the men come up and take a paper out of the box. Keep the paper folded in your hand without looking at it until everyone has had a turn. Everything clear?

As we see, after the Hutchingsons have drawn the marked paper, then each member has to draw again to identify which one villager will be selected. Thus we could argue that this sequential system of selecting somebody means that an unfair system is created. Members of smaller families have a higher chance of being selected than members of larger families, as, in the way that families are selected, each family is considered to be equal to every other family, no matter how many people are in it. This could be the way that the system is unfair and the probability is skewed in the favour of people coming from large families.

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