The solution is much more intuitive if you use odds ratios instead of percentage probabilities. You go from a 99:1 ratio to a 98:2 (or 49:1) ratio.
In other words, it's another way of phrasing that it takes twice as much evidence to be 99% sure as it is to be 98% sure. Or that it's twice as hard to have 99% uptime than 98%.
> it takes twice as much evidence to be 99% sure as it is to be 98% sure.
Not twice as much evidence. Evidence needs to be measured logarithmically. (Otherwise you'd say it takes twice as much evidence to be 67% sure as 50% sure (2:1 versus 1:1), but the second takes no evidence at all for a binary proposition.)
It takes twice as much evidence to be 99% sure as 91% sure. 98% to 99% is 17 decibels to 20 decibels, which is less than 20% more evidence.
This paradox also helps illustrate why you might want to avoid percentages or 0-1 decimal probability in statistics - in some cases, the compression at the end of the range can mask very important phenomenon. (0.01% and 1% look almost the same as percentages or decimals, but can have different implications.) Particularly important if you're doing anything at the tails of the distribution, like thinking about how to increase extreme values (is increasing the proportion of extreme-values from 0.01% to 0.10% extremely important or utterly trivial?)
Good observations. Look at how much easier it would be to solve this version of the Martian potatoes problem which avoids percentages altogether:
Earth has developed an insatiable appetite for Martian potatoes with their tasty pulp. Yuki runs a successful manufacturing plant on Mars which synthesizes a product called 'Martian Instaspuds'; instant potatoes being more cost effective to ship. Now these red potatoes (it's Mars after all) are processed in lots of 100kg mass which consist of 1kg pulp to 99kg water, 1p:99w. For 'Instaspuds' this ratio must be reduced to 9p:1w. How much water must be boiled-off in solar powered kilns on the Martian equatorial surface to achieve this ratio?
1) posit the pulp mass remains constant at 1kg
2) x = end product mass; 9/10 x = 1kg; x = 10/9 kg;
1/9 kg = final water mass in resulting mixture
In other words, it's another way of phrasing that it takes twice as much evidence to be 99% sure as it is to be 98% sure. Or that it's twice as hard to have 99% uptime than 98%.