Suppose that a barrel contains many small plastic eggs. Some eggs are painted red and some are painted blue. 40% of the eggs in the bin contain pearls, and 60% contain nothing. 30% of eggs containing pearls are painted blue, and 10% of eggs containing nothing are painted blue. What is the probability that a blue egg contains a pearl?
Who cares, where are the chocolate ones?
ReplyDeleteI'm with Adullamite on this one. Plastic eggs are not for me.
ReplyDeleteThis is math, isn't it?
ReplyDeleteI hate math.
We don't know the total number of eggs or percentage of the eggs that are red (Y)or blue (X).
ReplyDeleteWhat we know is that
Pearl (P)= 0.4(X+Y)
NonPearl (NP)=0.6(X+Y)
X = 0.3P +0.1NP
Y = 0.7P + 0.9NP
From the latter, on can discover that Y=4.56X (I'll skip all the steps 'cause I'm lazy)but that's not necessary because the relative percentage is going to be .4*.3:.1*.6 or .12:.06 or 2:1 pearls.
One can actually get percentage of red vs. blue as well and the relative number of pearl:nonpearl for red as well, everything, in fact, except the total number of eggs.
Hint: your odds are better if you can fish out a blue egg, considerably better.
I didn't know there would be a quiz.
ReplyDeleteThe question, in this form, is unanswerable, because it tells us that "some eggs are painted red and some are painted blue", what it does not say is that ALL of the eggs are either red or blue painted. It is thus possible that in fact most of the eggs are yellow.
ReplyDeleteAlso, the question asks what is the probability of a blue egg containing a pearl.
Let us look at the possibility that some of the unknown eggs are actually self-coloured blue, and not painted.
The information about what proportion of painted blue eggs contains a pearl would give us no clue whatsoever as to the probability of a blue egg containing a pearl. Unless the question clearly states that there are ONLY blue and red painted eggs....
What follows is the untutored-in-math reasoning of Relax Max:
ReplyDelete1. 40% of all eggs contain pearls.
What does this mean? One thing it means is that if color were not a factor, you could put your hand in the barrel and pull out an egg at random and there would be a 40% chance of that egg having a pearl in it.
But color DOES matter.
2. 30% of pearl eggs are blue.
What does this mean? It means, for one thing, that 70% of pearl eggs are painted red. But forget that.
3. The fact that 40% of all eggs contain pearls does not mean, necessarily, that 40% of all BLUE eggs contain pearls. Even I can see that.
4. If you ARBITRARILY say the barrel contains 100 eggs (it doesn’t matter how many eggs are really in the barrel since we are dealing only with percentages here; I learned that a long time ago), then:
a. 40 eggs contain pearls and 60 do not.
b. 30% of the 40 pearl eggs (12) are painted blue. (12% of ALL eggs are both blue and have a pearl inside.)
c. If 12 blue eggs contain pearls, and 10% of all non-pearl eggs are also blue: 10% of 60 is 6 empty blue eggs...
d. And it then follows that there are 18 blue eggs total, 12 with pearls in them and 6 empty.
e. This means that if you pick up a blue egg at random, the chance of it having a pearl inside are 12 times out of 18, or 12/18 or 2/3 or .6667 of the time.
I am not schooled in much more than basic math, so the above is how I arrived at my answer (which turns out to be right), like a 5th grader using logic rather than memorizing mathematical formulae.
Rest assured, though, that the webiste I got this problem from has enough mathimatical formulas to make my friend Rocket Scientist beam with pride, and if you would like to see those formulas for this problem, you can look at them at
http://yudkowsky.net/rational/bayes (Scroll down to this problem below the beginning problems on that page.)
Sadly, my juvenile logic wasn’t sufficient to solve the first couple of problems. Or even follow what the guy was trying to say.
This website was talking about something called “Bayes’ Theorem," but they lost me on that pretty quickly.
Ah, Soubriquet, it was that kind of thinking that makes true/false tests the bain of my existence (though I don't run into those any more now that I'm a "grown-up"). Technically true, but I would still have been able to do this with their implied meanings.
ReplyDeleteHaving said that, I used to drive my statistics teacher nuts with my questioning the conclusions they drew from observations and what the meant for predicting probabilities. For example, they had a problem: If you went to Venus and found Venusians and stayed for ten days, and, during those days X amount of Venusians died, how many Venusians would you have to take with you, duplicating the conditions exactly, to be *assured* that at least one would survive the trip.
I told him his problem was unsolvable. First, there's no way you could duplicate living conditions exactly. Not only is Venus too hot to duplicate readily, just gravity varies during a space flight and we don't know that changes in gravity could kill them.
But ten days with living things doesn't tell you jack on what their life expectancy would be. Perhaps they're like cicadas and all die within a certain time frame. If we caught the beginning of the death wave, they'd all die, etc. There was more but I'll stop there.
My teacher thought I was a pain in the butt
@ RM,
ReplyDeleteBayes theorem is part and parcel of statistics. You were better of trying to wipe that from your mind.
Soubriquet's comment was so good I'm going to play off it and this post write an actual blog post of my own (no, really!) on the dangers of statistics.
ReplyDeleteOh, by the way, one of the things that can be discerned about the total number of eggs (assuming the problem can be taken at face value) is that the total number of eggs actually *can't* be 100.
More on my post when I write it.
@Adullamite - At least you are not being rude today. Chocolate eggs only come out at Easter, brought by the magic bunny who was frightened at the sound of the stone being rolled away. Or so legend has it.
ReplyDelete@A. - Some plastic eggs contain pearls.
@Linda - I thought it was math. Turns out its statistics. Give it a try anyway. :) Loving your blogs. You have really evolved into a pro writer and photographer, you know. Soon you will get the big bucks for that. Just stay the hell away from Claire.
@Stephanie - Greek to me. You are probably right. I wouldn't bet against you on math or metrics.
Math is hard.
ReplyDeletePhew. I thought for a while that I was the only one who could seen the king's undercarriage.
ReplyDeleteI must thank Ms Barr for her support.
My grandfather loved to plague me with conundrums (conundra?), asking questions like " If it takes one man three hours and seventeen minutes to dig a hole three feet wide, four feet three inches long, and six feet eight inches deep, how long would it take three men to do it?
"Aha!", I'd think, and say, quick as an arithmetically-challenged child can, "One hour, five minutes, and forty seconds!".
I would expect praise. But of course, he'd shake his head wearily. "Nay, lad, there's nobbut room for one man in't hole."
Which early training has led me to suspect every question needs to be carefully inspected for similar traps.
Sometimes the question is framed in such a way that without further information it can not be answered.
Now I'll go see what she's written about statistics.
It's 'MATHS' by the way.....
ReplyDelete@Sue - Math is not hard for me. Astrophysics is not hard for me. Psychology is not hard for me. I have long ignored them and still survive, after a fashion. I recommend you do the same. :) 2 dolla for 1 shirt. That's all the math you need to know.
ReplyDelete@Adullamite - No, there is only one math problem. It is a mathematical problem. Math is short for mathematical. :) :) :)
I took a college class in Statistics once and barely passed it as it was too close to math I'm afraid!
ReplyDeleteThanks for the lovely compliments but as for staying away from Claire no can do as I'll be giving her the grand tour of New England later this year.
Oh dear!
Re-thought my answer.
ReplyDelete100%.
It's right. I expect to graduate with honours from the University of Max, or it'll be fisticuffs at dawn.
Agh! No! You're probably bigger than me and more agile.... I shall tailor my challenge to my better advantage.
like... um..
Well, I'll think of one, eventually.
@Linda - Be sure and take her to Salem. :)
ReplyDeleteNo stats or math required here, though.
@Soubriquet - definitely close enough for this kind of thing.
ReplyDelete