= 27d567bc2d48d9f40e9ccc20ea370b15)
Emile comments on Probability updating question - 99.9999% chance of tails, heads on first flip - Less Wrong Discussion
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (16)
It seems some information is missing, so I'll try reformulating the problem my way:
P(fair & heads) = 0.01 * 0.5 = 0.005
P(unfair & heads) = 0.99 * 0.001 ~= 0.001
so P(heads on first throw) = 0.006
so P(fair | heads on first throw) = 5/6
so P(heads on second throw | heads on first throw) = 5/6 * 0.05 + 1/6 * 0.001 ~= 0.42
... at least, that's one way of interpreting "you are 99% confident in your results", I consider that the remaining 1% is "your analysis was completely wrong and the coin is just as likely to land on heads or tails". A more realistic situation would be one where your confidence would be distributed among possible coins in coinspace, something like "90% confident of less than 0.01% odds for heads, 99% confident in less than 1% odds for heads, 99.9% confident in less than 10% odds for heads, etc.".
I like the reinterpretation of the problem, but is
a typo? Just running the numbers through SpeedCrunch gives 0.99 * 0.0001 = 0.000099, and 0.000099 ~= 0.0001, which seems intuitively right as 0.99 is "almost" 1.
Augh! Serves me right for modifying the values while writing the comment and not thoroughly rechecking the calculations, thanks!