Do This by Logic
 

Again I am trying to get you to think, not blindly use formulas. You reach into a bowl that you know contains three fair coins and one double headed coin. You randomly pick one. Without looking at it, you flip it two times and get two heads. What's the chances you picked the bad coin?

33% *NM*
 

Ignore above...
 

...I thought it said 2 fair coins, not 3. So my answer would be 25%.


Ryan

Re: Ignore above...
 

I dont think 2 flips of heads, would be a big enough sample to change any percentage. There are 3 regular coins and one bad (1 out of 4) thats why I say 25%. Now if it came up 12 times in a row, then your odds would be almost 100%.

4 / 7
 

The funny coin will be picked 1/4 of the time. A fair coin will be chosen 3/4 of the time and come up heads twice 1/4 of the time, which means this sequence occurs 3/4 * 1/4 = 3/16 of the time. Thus, HH will appear 3/16 + 1/4 = 7/16. So the probability that HH is caused by the funny coin is 1/4 / 7/16 = 4/7.

A wild guess ...
 

... is 4/7 !?

Re: Do This by Logic
 

First try:


The chances you would initially pick a fair coin are 3/4. The chances that a fair coin would flip two heads in a row is 1/4. So the chances that you picked a fair coin AND flipped 2 heads in a row with it is 3/4 * 1/4 = 3/16. Therefore the chance that you picked the double-headed coin is 13/16, since 3/16 plus 13/16 = 1.0


Intuitively this seems high, so I am going to think about it a bit more while I go out for a bit of exercise.

Re: Do This by Logic
 

25%

The fact that no tail came up only proves that it is possible that you chose the double headed coin.

How'd I do?

Of Course That\'s Wrong
 

I was erroneously counting the ways that it might have not been two heads in a row as belonging to the double-headed's claim.


Out of a total of 16 possible picks and flip sequences, 4 give two heads with the double headed coin. 3 give two heads with the single headed coins. Therefore the odds are 4/16 vs. 3/16 which reduces to 4:3 in favor of the double-headed coin. (I believe we must count the double-headed coin as having two distinct sides even though both sides give the same result).

Re: Do This by Logic
 

One in four that you chose the bad coin.


Jimbo