Do This by Logic

there are four apples in a basket


one of them is laced with sleeping potion


a guy picks one at midnight and eats it


he falls asleep


another guy takes a bite and he falls asleep


what is the probability that this is the funny apple?

1/4 assuming they would fall asleep at midnight regardless.

bit slow as usual but i think i understand it now


the result that you see is HH


although there were two events leading up to this result the first event of picking has long gone under the bridge


the way you can have such a result is by the H/h coin falling HH, Hh, hh, or hH, or the three H/T coins falling HH


so there are seven different possible forms of the HH you can see, four of which could be made by the H/h coin and three by the H/T coins


hence 4 out of 7 times that you do see HH it is as the result of having picked the H/h coin

what are the chances you picked the bad coin, not what are the chances you picked the bad coin and flipped it twice and came up with two heads. I think no matter how many times you flip heads, until you flip tails the answer is still 1 in 4...i think

The fact that the coin came up HH twice is relevant.

For instance, if you knew that after flipping the coin twice that it came up TT, the probability that it is the bad coin is 0 (even though initially the probability of picking it was 1/4).

Since two flips won't indicate anything, probability-wise

3 fair coins each have 1/4*1/4

1 bad coin has 1/4 chance of being flipped 2 heads


3/16 chance that fair coin was flipped 2 heads

1/4 chance that bad coin was flipped 2 heads


thus prob of bad coin is 4/7


peter

Funny, i got the number 4/7, by a different route (I think) to most others...only read a few after I did it myself.


Fair coin gives HH 0.25 of time. Funny coin 1.0 of the time. Just compare the added probabilities for fair and funny coins (ie 0.75 cf 1.0 or 4/7).

cf ?