wishIwasSalludon
broken but not destroyed
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- Nov 9, 2023
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The "paradox" is as follows
1. a fair coin is tossed on Monday
2. if it lands on heads sleeping beauty is awoken on Tuesday then put back to sleep
3. if it lands tails she is awoken on Tuesday has her memory erased then awoken again on Wednesday
Each time she is woken up she is asked "what is the probability the coin landed on heads?"
Some people say a third the other 1/2 these views are called thirders and halfers respectively. The way thirders justify their view is that there are two days where the coin is on tails and another on heads so the chances of the coin being heads is 1/3.
Sounds reasonable except the problem is now you've said the probablity of a coin toss landing on heads is 1/3 which doesnt make any sense... we can take this argument even further imagine given tails sleeping beauty is awoken 1000 times instead of just twice. Does that mean now the chances of a coin landing on heads is 1 in 1001?
The problem is thirders are treating the two days sleeping beauty is woken up given tails as seperate events. Remember she is only woken up twice GIVEN the coin lands on tails they are not independent events so you cant use the typical equation for probability. What thirders are describing is the chances of sleeping beauties guess of heads being correctly given she is woken up this is not the same as the chance of the coin landing on heads or tails.
The reason why sleeping beuaty is more likely to answer correctly if she says tails is because she is woken up more times given the coin lands on tails. So the chances of sleeping beauty answering correctly and the chances of the coin landing either heads or tails is no longer the same since we have added a condition.
It's insane how this is considered a paradox when the answer is so fucking simple
@SlayerJonas @imontheloose @Wicket @Mainlander
1. a fair coin is tossed on Monday
2. if it lands on heads sleeping beauty is awoken on Tuesday then put back to sleep
3. if it lands tails she is awoken on Tuesday has her memory erased then awoken again on Wednesday
Each time she is woken up she is asked "what is the probability the coin landed on heads?"
Some people say a third the other 1/2 these views are called thirders and halfers respectively. The way thirders justify their view is that there are two days where the coin is on tails and another on heads so the chances of the coin being heads is 1/3.
Sounds reasonable except the problem is now you've said the probablity of a coin toss landing on heads is 1/3 which doesnt make any sense... we can take this argument even further imagine given tails sleeping beauty is awoken 1000 times instead of just twice. Does that mean now the chances of a coin landing on heads is 1 in 1001?
The problem is thirders are treating the two days sleeping beauty is woken up given tails as seperate events. Remember she is only woken up twice GIVEN the coin lands on tails they are not independent events so you cant use the typical equation for probability. What thirders are describing is the chances of sleeping beauties guess of heads being correctly given she is woken up this is not the same as the chance of the coin landing on heads or tails.
The reason why sleeping beuaty is more likely to answer correctly if she says tails is because she is woken up more times given the coin lands on tails. So the chances of sleeping beauty answering correctly and the chances of the coin landing either heads or tails is no longer the same since we have added a condition.
It's insane how this is considered a paradox when the answer is so fucking simple
@SlayerJonas @imontheloose @Wicket @Mainlander
