/sci/ - Science & Math

people say you had a 1/3 chance of picking the car in the first choice so that must mean it was a 2/3 chance of being wrong so you're more likely to win by switching,
but you also had a 1/3 chance of picking a specific goat, like if the goats had names Ray and Charles.

[car] [ray] [charles]

the game doesn't care about your initial pick, it will always reveal either [ray] or [charles] and ask if you want to pick again between what is left over.

you had a 1/3 chance of picking the car
you had a 1/3 chance of picking ray
you had a 1/3 chance of picking charles

if charles is revealed, then the game becomes:

you had a 1/3 chance of picking the car
you had a 1/3 chance of picking ray

and since theres only 2 options left, the odds change:

you have a 1/2 chance of having picked the car
you have a 1/2 chance of having picked ray

you did not pick both ray and charles if you picked either ray or charles initially. ray and charles together are 2/3, and the car is 1/3, but ray doesn't become two goats if charles is removed, and neither does charles become two goats if ray is removed.