Coomb t1_its9nxp wrote
Reply to comment by eth_trader_12 in How does one figure out what probability is most relevant when deciding how probable something is? by eth_trader_12
>I completely agree with you except the last statement. P(R|A) given the same principle of more information that you just said assumes that "all the information" we have is that someone at some time won two lotteries twice. As in, if you knew that someone won two lotteries at some point or another, then yes, P (R|A) would suffice. > >But in this case, we know that Juliet won. Hence, we calculate P (R|J), even if we don't know anything else about Juliet
Why? Why do we do that when as far as we know Juliet is no different from anyone else? There is no more reason to assume the lottery is rigged because a particular individual whose name you know won twice in a row if you know nothing at all about that individual. If you don't know them from Adam, then Juliet could just as easily have been Adam or Bobby or Charles or Doug. Knowing literally nothing other than her name is the same as knowing nothing at all about her, unless the lottery is rigged for anyone named Juliet and you know that.
eth_trader_12 OP t1_itsfkc8 wrote
That’s what you’re confusing. Looking at the specific probability of Juliet winning the lottery twice does increase the probability that it is rigged, just perhaps not enough. The only reason many consider it still not rigged is because of prior probabiltiies: the vast majority of lotteries in history have been fair; very few have been rigged.
But now imagine as if half of all lotteries were fair and half were all rigged. Let’s assume 10,000 tickets and 10,000 people. Let’s now look at the first case the other commenter mentioned: Juliet won the lottery once. The prior probabiltiies are the same for rigged and fair so they can be ignored. We now look at the likelihoods. The probability of Juliet winning the lottery given a fair lottery is 1 in 10k. The probability of Juliet winning the lottery given a rigged lottery is ALSO 1 in 10k (given others could have rigged it). Fair lottery is equally as likely as a rigged one.
Now, let’s assume Juliet won the lottery twice. The priors are again the same so let’s look at the likelihoods. The probability of Juliet winning two lotteries given chance is (1/10k*1/10k). The probability of Juliet winning two lotteries given that it’s rigged is 1/10k (1 out of 10k people could have rigged it twice). Now, the rigged lottery is MORE likely. Note that if we looked at the more generic description of SOMEONE winning the lottery twice, the likelihood of SOMEONE winning the lottery back to back would be 1…given enough time. But the likelihood of SOMEONE winning the lottery back to back given its rigged..is also 1. Now we must conclude they’re equally likely, but that’s not accurate.
As you can see; looking at specifics seems to work better.
pucklermuskau t1_itv0hxz wrote
what difference does it make that you know her name?
eth_trader_12 OP t1_itvas30 wrote
It doesn’t. You missed the entire point of the example. Even if I didn’t know her name, I would know that a specific person won it, and the math would be the same.
The math would be different only if I knew that someone at some time won two lotteries, not at a specific time. The time is what’s relevant here
pucklermuskau t1_itvbekr wrote
in all examples that are being discussed, those that you're strangely dismissing, we are assuming that the same person has won twice in a row. you're misunderstanding the argument.
[deleted] t1_itvxksv wrote
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