A mad scientist

Originally posted by smomofo
Actually, it might be 1/5.

I would go with 1/5 also

Originally posted by PBE6
Each of the above occur with probability 1/4.

But there is no a priori evidence for that. 🙄

Originally posted by ThudanBlunder
But there is no a priori evidence for that. 🙄

They're all equally likely (assuming a random drawing of course), and there are 4 possibilities, so each one has a probability of 1/4. If the drawing was not completely random, the problem should have said so, otherwise any answer can be justified with a cock-eyed backstory.

Originally posted by Keltamaksa
Here's a little snack-sized puzzle. I saw this on a science magazine some years ago and modified it a little.

You're in a lab of a mad scientist. You see two identical containers on the table but you can't see their contents. When you look at the scientist, you notice that he's holding a fresh human brain in his hands. "One of those containers", he say ...[text shortened]... ainer he had picked. "With what probability does that jar have another brain in it?"

1 out of 8

Have you given the answer yet?

Originally posted by PBE6
They're all equally likely (assuming a random drawing of course), and there are 4 possibilities, so each one has a probability of 1/4.

The question is how were they put in the box?
For example, you throw a die.
If it comes up a 1 or 2, you put SS in the box;
Otherwise, you put SG in the box.
(Or you could do it the other way round. Or use another method to get whatever probabilities you choose.)

Without any a priori information on how the coins were put in the box, any purely numerical answers will be based on unjustified assumptions.

When this puzzle was doing the rounds about 20 years ago the usual answers were 1/2 and 2/3. However, there is also 'not enough information' which is the answer I agree with.

Originally posted by Keltamaksa
"One of those containers", he says, "has either a liver or a brain in it. The other one is empty."

This statement tells us nothing of the probability of there being either a liver or a brain in the container. Without that information, the problem is not solvable.

Originally posted by ThudanBlunder
The question is how were they put in the box?
For example, you throw a die.
If it comes up a 1 or 2, you put SS in the box;
Otherwise, you put SG in the box.
(Or you could do it the other way round. Or use another method to get whatever probabilities you choose.)

Without any a priori information on how the coins were put in the box, any purel ...[text shortened]... /2 and 2/3. However, there is also 'not enough information' which is the answer I agree with.

In this problem, the box contains "exactly two coins", so you can't fudge it by placing only one coin in the box.

Your point about the nature of the "random" draw is correct; we must have accurate information on the probability of each event if we are to come up with the correct answer. But at the same time, we should be reasonable in assessing these puzzles. In the absence of evidence to the contrary, it is perfectly acceptable to assume the draw is random.

Originally posted by SiteNine
This statement tells us nothing of the probability of there being either a liver or a brain in the container. Without that information, the problem is not solvable.

Again, you're reading too much into the question. Although technically the probability of the brain or the liver being in the container could be anything between 0 and 1, it's reasonable to assume that the chances are 50-50 for each.

If you don't like making that assumption, you should state your own and then go ahead and solve the puzzle.

Originally posted by aging blitzer
I would go with 1/5 also

I tried running an Excel simulation on the brain/liver puzzle just to confirm the answer. In the simulation, I seeded Jar 1 with either a brain (RAND()0.5), and then chose Jar 1 (RAND()0.5) at random to add the brain. A random jar was then chosen in the same way, and a random organ was chosen. If the jar was empty, the result was "empty"; if the jar contained only one organ, that organ was chosen; and if the jar contained two organs, one was chosen at random (50% chance of either one being chosen).

Always seeding Jar 1 with the first organ does not affect the answer, because the final jar is chosen at random later on.

After running 60,000 trials, a brain was picked 563.0 times on average (standard deviation 2.9% of total), and of those times the brain was drawn from the double brain jar 126.8 times on average (standard deviation 8.2% of total). 126.8/563.0=0.225, which is within 1.4% of my previous answer of 2/9=0.2222, so I'm confident in it.

Originally posted by Fat Lady
Can the containers hold two objects? i.e. Could he have initially put the brain he was holding into the container already holding a brain or liver?

Hello 😉

Originally posted by PBE6
In the absence of evidence to the contrary, it is perfectly acceptable to assume the draw is random.

...provided this assumption is not presented as a fact.

The question is ambiguous, in that, the scientist states that 'one of the jars has a liver or brain in it'. We have no information about what is in the other jar.
However, the statement implies that the othe is empty. Working on this assumption it is a 1 in 2 chance that the jar contains anything, and a further one in two chance that it is a brain and not a liver in the 'occupied' jar. Which means that it is a 1 in 4 chance of the two brains colliding.

Originally posted by ThudanBlunder
A box contains exactly two coins, either two Silver or one Gold and one Silver. A coin is chosen at random. It is Silver.
What is the probability that the other coin is also Silver?

50%

I think the major problem with all the simulations you guys are trying to run is that you are calculating "What are the chances that if I pick a jar at random it has two brains in it?"

Consider flipping a coin, it can land heads or tails.

Now if you have flipped a coin 10 times and it landed heads everytime, what are the chances it will land heads when you flip it the 11th time? ... right 50% since you're only looking at the chances of flipping this coin once.

It will be different if you were to try and calculate the chance of a coin landing heads 11 times in a row (0.048828125😵

Originally posted by ThudanBlunder
A man has exactly two children. At least one of them is a boy.
What is the probability that both his children are boys?
----------------------------------------------------------------------
A woman has exactly two children. The older of the two is a boy.
What is the probability that both her children are boys?

Impossible to answer correctly since sex is determined by genetics. Both the man and the woman can have weak or strong biases toward male or female children that would skew the probability.


50% is the answer to this flawed question however.