Hi,
I came across a probability question I thought was interesting :
"You volunteer to undergo the following experiment : On Sunday you will be put to sleep. Once or twice, during the experiment, you will be wakened, interviewed, and put back to sleep with an amnesia-inducing drug that makes you forget that awakening. A fair coin will be tossed to determine which experimental procedure to undertake: if the coin comes up heads, you will be wakened and interviewed on Monday only. If the coin comes up tails, you will be wakened and interviewed on Monday and Tuesday.
During the experiment – you are wakened and have no idea if it is Monday or Tuesday. You are asked to estimate the probability (given you have found yourself awakened) that the coin landed heads. What is your answer?"
There are two schools of thought about this – one group of people say 50% - the initial probability of heads was clearly 50% and you have been given no new information to change that. The other school of thought says 33% - if you repeated the experiment many times you would find that only 33% of the time you are wakened it was heads.
Points to consider :
- If tails leads to 100 wakenings rather than just 2 – would that convince you that tails was much more likely than heads?
- The coin toss doesn’t have to be made until Tuesday morning – ie when you are wakened it might be Monday and the coin toss will be done tomorrow. Are you really going to say something other than 50% for probability of heads from a fair coin which might not even have been tossed yet?
Note - I didn't invent this - its been much discussed apparently - but I hadn't seen it here before and thought it was interesting so you lot might appreciate it :).
- Drelda
I came across a probability question I thought was interesting :
"You volunteer to undergo the following experiment : On Sunday you will be put to sleep. Once or twice, during the experiment, you will be wakened, interviewed, and put back to sleep with an amnesia-inducing drug that makes you forget that awakening. A fair coin will be tossed to determine which experimental procedure to undertake: if the coin comes up heads, you will be wakened and interviewed on Monday only. If the coin comes up tails, you will be wakened and interviewed on Monday and Tuesday.
During the experiment – you are wakened and have no idea if it is Monday or Tuesday. You are asked to estimate the probability (given you have found yourself awakened) that the coin landed heads. What is your answer?"
There are two schools of thought about this – one group of people say 50% - the initial probability of heads was clearly 50% and you have been given no new information to change that. The other school of thought says 33% - if you repeated the experiment many times you would find that only 33% of the time you are wakened it was heads.
Points to consider :
- If tails leads to 100 wakenings rather than just 2 – would that convince you that tails was much more likely than heads?
- The coin toss doesn’t have to be made until Tuesday morning – ie when you are wakened it might be Monday and the coin toss will be done tomorrow. Are you really going to say something other than 50% for probability of heads from a fair coin which might not even have been tossed yet?
Note - I didn't invent this - its been much discussed apparently - but I hadn't seen it here before and thought it was interesting so you lot might appreciate it :).
- Drelda
via JREF Forum http://ift.tt/1fkwkoJ
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