"Is "-1 against" the same as "+1 for"? Expressi..."


by Dewi Morgan Sep 25 2018

Answer 89% is around 8 times as much as 11%, so we start out with $~${^-3}$~$ bits of belief that a random oyster contains a pearl\. Full oysters are 1/2 as likely to be blue as empty oysters, so seeing that an oyster is blue is $~${^-1}$~$ bits of evidence against it containing a pearl\. Posterior belief should be around $~${^-4}$~$ bits or $~$(1 : 16)$~$ against, or a probability of 1/17\.\.\. so a bit more than 5% \(1/20\) maybe? \(Actually 5\.88%\.\)

Is "-1 against" the same as "+1 for"?

Expressing the first practical example entirely in terms of negative numbers seems like a poor pedagogical choice.

Phrasing as "3 bits against" and then "a further 1 bit against" may help.

Adding that the blue ones are not a great pick if you want pearls may help people understand the direction of "against".