"Square One" was an awesome show. I liked "Mathnet" the very, very best. I have no issue with the gist of this article about opportunist idiotface John Edward, but author Shari Waxman mustn't have passed her probability and statistics class:
"[The summation law of probability] states that the calculated probabilities of events that are independent (i.e., the occurrence of one event has no effect on the probability that another event will occur) may be added together. In symbolic terms, where A is the first event, B is the second event and P stands for probability: P(A) + P(B) = P(A or B)
"For example, if you roll a six-sided die betting on a 3, your chances for success are 1 in 6, or 17 percent. Roll the die six times, and you are almost guaranteed to see a 3 (17 percent x 6 = 102 percent). Lucky for Edward, most audience members on his television show, "Crossing Over," are too hopeful and trusting to pull out a calculator and expose the charlatan behind the prophet."
Alas, Ms. Waxman missed one little tidbit about the summation law of probability. The events don't have to be independent. The events have to be mutually exclusive1. For example, if RunRunRunBabyBabyBaby has a 1 in 5 chance of winning a race, and IAmASlowHorseBecauseILikeGrassTooMuch has a 1 in 20 chance of winning the same race, one adds 1/5 + 1/20 and volia! there is a 1 in 4 chance of either of the two horses winning the race.
In Ms. Waxman's example, however, while the events are independent, they are not mutually exclusive; one could roll a three with toss number two and with toss number four. So we have to use a different formula: the double inverse multiplicative law of probability. (It probably has a proper name, but I'm sure I like mine better.) This formula says that when you have independent events with probabilities A, B, C, ..., Z, the probability of at least one of those events occurring is:
1-(1-A)*(1-B)*(1-C)*...*(1-Z)
I could tell you why this works, but I won't.2 Anyway, using this law, with A=B=C=D=E=F=1/6, we get a 66 percent chance of at least one three, not -- ahem -- the ludicrous 102 percent.
I'm sorry for this unfun diversion, non-math people.
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1 Fun fact: By definition, mutually exclusive events cannot be independent.
2 Okay, I will, but only in this footnote. To get the chance of all of a series of independent events occurring, one simply multiplies the probabilities: A*B*C*...*Z. One step further: to get the chance of all of a series of independent events not occurring, one multiplies together the chances of each of the individual events not occurring: (1-A)*(1-B)*(1-C)*...*(1-Z). And because having at least one event occur in a series is the opposite of having no events occur in a series -- one of those two statements has to be true, one just takes one minus the...oh, forget it. None of you care about this. Y’all just want more booger and poop jokes.
oh so lovingly written by
Matthew |
i sincerely do not know what you are doing here. are you lost? were you
looking for your delicate calico cat, and did you follow her up two flights of stairs
to this room? she is not here. she was here, yes. we gave her a warm bowl of milk, we talked with her about campaign finance reform for a time, and then she bid us good day. i believe she was
going to the post office two blocks down, but i don't quite recall.
for surely you did
not find your way from prinsiana, the least traveled site on
the internet. if you did, though, perhaps you are looking for humor. perhaps you are looking for profundity. perhaps you are looking for answers.
i'm sorry, but you shall go naught-for-three.
