Does this probability question admit an answer?

[ultrafilter]

Sorry, my mistake. I read the experiment and jumped straight to the Monty Hall fallacy. Mea culpa.

But the probability didn’t change because of your knowledge–it changed because the set of possible outcomes changed.

[Nightime]

Monty’s Law: As an online discussion on probability grows longer, the probability of a reference to Monty Hall approaches one.

[spingears]

@Nightime

r = original number of red marbles
b = original number of blue(corrected) marbles
probability of picking a red marble = (r + 3)/(r + b + 5)

CORRECT This is the PROBABILITY of picking the specified color.
For the spinners…Whoooosh :rolleyes:
Reread the original question.
It is a question of probablility, NOT of how many Red or Blue original marbles!

[Frylock]

But to say “the set of possible outcomes changed” just is to say my knowledge of the situation changed… isn’t it?

In other words, the word “possible” in the phrase “possible outcomes” just means “concievable according to my state of knowledge regarding the placement of the cards.” (Not saying that’s what “possible” always means, just saying that’s what it’s meaning cashes out as in this particular situation.)

-FrL-

BTW I spent a week or two trying to prove the person who introduced me to Monty Hall’s paradox wrong. Now it’s others who spend a week or two trying to prove to me that it’s wrong. And the circle of life goes on…

@ultrafilter

Sorry, my mistake. I read the experiment and jumped straight to the Monty Hall fallacy. Mea culpa.

But the probability didn’t change because of your knowledge–it changed because the set of possible outcomes changed.

[Valgard]

@Lazy Dragon

For all Frylock knows, you may equally likely be the kind of person who puts in a marble only 10% of the time. If Frylock has no way of preferring one alternative over the other, from his point of view, both alternatives are equally likely. Another example: Frylock tosses a coin, and you, Valgard, look at it. Seeing that it’s tails, from your point of view the likelihood of tails and heads are 1 and 0, respectively. From Frylock’s piont if view it is still 50/50.

If you have no way of knowing which way the process is biased, both ways are equally likely (from your point of view), and the likelihood of red/blue is 50/50.

There seems to be some misunderstanding going on that there is some real, underlying probability distribution that you have to know in order to make probability calculations, but the whole point of these calculations is to infer from incomplete knowledge. If you look at my example of the coin toss above, it is clear that, given Frylock’s information, the probability is 50/50, and from Valgard’s it is 100/0.

To put it into other words: If you have no information about the probability distribution, then every distribution is equally likely, leading to a flat (uniform) distribution.

No, this is just wrong. If you want to make a calculation about probabilities you have to know some basic info about the underlying PDF and the OP as stated doesn’t contain the info you need. If you don’t know the distribution and you make a guess at it, then all of your calculations based on that are just guesses as well. GIGO!

@Lazy Dragon

0.5 that it’s 2, 0.5 that it’s 3, leading to an expected value of 2.5 (really.)

Frylock wasn’t calculating an expected value, he was calculating a probability. They are two totally different things. If you KNOW that the two outcomes have equal probabilities then your calculation is correct but you don’t know that at all.

@Lazy Dragon

To address the OP:
If you have no way of knowing the number or red/blue distribution of marbles, then it is equally likely that the red outnumber the the blue, as the other way around, so you would expect there’s an equal number of each. As to the total number: if every number between 0 and infinity is equally likely, then there will, with probability 1 be an infinite number of marbles in the bag, leading to a 50/50 probability of drawing a red versus blue marble.

This is, however, misleading. You do have some information about the number of marbles–using common sense. There isn’t room in the universe for an infinite number of marbles–much less in a bag. You have to make an educated guess of a reasonable upper limit of marbles. You can call this upper limit L, and frame your answer in terms of L, using methods described by other posters, or, alternatively, you can posit some probability distribution on L, and include this in your calculation.

The reason this problem becomes complicated is the number L. If you have no information about a quantity, assuming a flat probability distribution is the way to go, but with L you clearly know that the PD must decrease and go to zero. The problem needs to be more clearly stated as to what kind of information you get. Are you allowed to see the bag, etc…

Gotta disagree here. Again, you can assume any distribution that you want but your answer is only as good as your assumption. If your assumption is a guess then your answer is a guess. Period. If you want to have an actual numerical result then you have to know the actual PDF. There’s NO way around it barring the case of “Suppose that there’s approximately equal and very large numbers of reds and blues”, that’s just a mathematical limit.

[Hooleehootoo]

@Pasta

A Frequentist is one who uses impeccable logic to draw conclusions with which everyone agrees and about which no one cares. A Bayesian is one who answers questions in which everyone is interested by using assumptions that no one believes.

I would like recommendations for books discussing Frequentist and Bayesian philosophy. Something akin to the writings of Ivars Peterson or Martin Gardner.

I have “The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century” by David Salsburg. I did not like this book as much as I had hoped to. As I recall, it does not talk about Frequentism and B-ism.