Heads or Tails?
A box contains two coins. One coin is heads on both sides and the other is heads on one side and tails on the other. One coin is selected from the box at random and the face of one side is observed. If the face is heads what is the probability that the other side is heads?
Labels: mathemagic
posted by Chris at
3:06 PM
13 Comments:
There are three heads in the box, I'll call them 1a, 1b, and 2a.
If a heads is drawn, it has a 2/3 chance of being on coin 1, so the final probability is 2/3
Well done Anonymous. That problem does most people's heads in.
There are 3 heads and one tails, so for the first pick, there's a 3 out 4 that it will be a heads. If it is a heads then there are 2 heads and one tails left. That would be 2 out of 3.
I think that was what anon said above.
Hi Ragknot, yours is the way that I see it.
While the probability that the other side of the coin is heads may be 2/3 i believe the probability that you grabbed the two headed coin would be 50%.
Hi Thrym. You're right in that the probability of grabbing the double-headed coin to start with is 1/2. But that isn't the situation being presented. That the face you're seeing is a head is crucial. In this case the probability that you have grabbed the double-headed coin is 2/3.
Compare with, if you had seen the tail; it would be probability 1 that the other side is a head and that you have the regular coin.
It's actually a formula in probability - Bayes' Theorem, which can anyways give the answer (without much thinking, ... if you know the formula :P). The answer comes 2/3 as said.
Yet, for the fun of it I would say that the probability is half - i.e. either the other side will be head or it won't be.(It can be proved that this statement is wrong, else, in universe everything will have the probability of occuring as half, i.e. either it will occur or it won't :))
Probabilities can be interesting and annoying. They are all a matter of perspective. I wasnt implying that 2/3 is wrong just that a different view can give a different answer.
"Lies, damned lies, and statistics."
If different views give different answers, then at best one of the views is right.
it would be 50%
it would be 50%
Hi kushal. What "it" are you referring to?
Post a Comment
Links to this post:
Create a Link
<< Home