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> Arguing that two outcomes are equally likely when one has happened many more times than the other is an exercise in frustration Are they actually equally lik
by jldugger 5y ago
> Arguing that two outcomes are equally likely when one has happened many more times than the other is an exercise in frustration
Are they actually equally likely though? Perhaps there comes a point where one must consider if observed outcomes match with assumed probabilities.
Or are you just having arguments about whether the unfavored outcome is 'overdue.'
- roenxi 5y agoFunnily enough, I might have been thinking of the exact opposite of the Gambler's fallacy. My mistake, sorry. But it still seems related to me and I'll explain what I was thinking anyway: For reference: https://www.omnicalculator.com/statistics/coin-flip-probability https://www.omnicalculator.com/statistics/coin-flip-probabil... There is a 20% chance that in 7 coin flips there will be >5 heads. By symmetry, 40% chance that there are >=5 heads or >=5 tails. If you look at a series of events (say, annual results) and one has exceeded the other in 5/7 years, that doesn't tell us that one is consistently better than the other. But people aren't good at accepting that.
- jldugger 5y agowell, i'd frame that conversation in terms of confidence intervals. with only 7 trials you are not very confident a>b.
- HWR_14 5y agoI found you text very confusing, and then figured out your typo. > There is a 20% chance that in 7 coin flips there will be >5 heads. By symmetry, 40% chance that there are >=5 heads or >=5 tails. Your first example should say >=5 heads. (Also, your site says almost 23%, making it just over 45% for either via symmetry)