"Price of hatching a Snorlax or Lapras"

#PokemonGO: After looking through some data* it looks like there's about a 0.5% chance for the egg you get from a pokestop to be either Snorlax or Lapras. I wanted to figure out how much one must spend on incubators in order to hatch one of these two rares.Here's the math:Let's assume we use paid incubators on all 5km and 10km eggs and infinite incubator on all 2km eggs. Let's then assume 20% of eggs you get are 2km.0.29% Snorlax, 0.23% LaprasAdded together is 0.52% chance. Divide this by 0.8 to get total percent out of only 5/10km eggs and you get 0.65%.Now let's do some probability and statistics:(1-.0065)106 = 0.5 = 50% chance of not hatching either (1-.0065)213 = 0.25 = 25% chance of not hatching either (1-.0065)353 = 0.1 = 10% chance of not hatching eitherThe numbers in the exponent is the number of hatchings using purchased incubators on 5/10km eggs. For example, this means is you have a 50% chance of hatching at least once of those two after 106 hatchings or about 36 incubators (5400 coins). So the cost to have a coin flip chance of getting either one of those two is about $40. For a 90% chance to get at least one you would have to buy 118 incubators or 17,700 coins!It's very important to know the math here is to get at least one. So that 90% chance mentioned includes all probabilities of getting multiple Snorlax and Lapras. The math to calculate just one hatch is more complex, probably requiring Bayes' theorem.Feel free to ask for clarification on the math or to dispute it. Pretty much I'm just doing chance to repetitively not hatch either and multiplying the chances of not hatching together. I'll add more numbers later for Snorlax and Lapras individually.*Data from http://ift.tt/2l3uxQr are the individual numbers (hatches not including 2km eggs):Snorlax50% chance, 191 hatches, 64 incubators, 9600 coins75% chance, 382 hatches, 127 incubators, 19,050 coins90% chance, 634 hatches, 211 incubators, 31,650 coinsLapras50% chance, 241 hatches, 80 incubators, 12,000 coins75% chance, 481 hatches, 160 incubators, 24,000 coins90% chance, 800 hatches, 267 incubators, 40,500 coinsFor those of you that have never hatched a Lapras and your native biome doesn't spawn it, you may be in that unlucky 10% that will need to spend more than 40K coins before getting one!! via /r/TheSilphRoad http://ift.tt/2jMP3j4