Each judge is asked to state which glass he most enjoyed.

[Isbell]

Hi, I'm sorry to have bothering you all again with a math problem:
"The manufacturer of a dairy drink wishes to compare the taste appeal of a new formula (B) with that of the standard formula (A). Each of 3 judges is given 3 glasses in random order, two containing formula B and the other containing formula A. Each judge is asked to state which glass he most enjoyed. Suppose that 2 formulas are equally attractive. Let X be the number of judges stating a preference for the formula B. Construct a probability distribution for X and find the probability that two of the judges state a preference for formula B."

I find it's not easy (if not hard) to understand the bold sentence and it turns out that I have two answer sets in an effort to find the probability of a judge stating a preference for the formula B. This isn't a good news because it confirms that I was wrong.

Could you please help me, if it's possible to enlighten me on how do you tell if a judge states a preference for formula B.

Any help would be much appreciated.

Thanks.

[Dozy]

Last time I tried to answer a maths-related question here I think I messed up, but here goes anyway...!

I think the question is badly formulated, and the answer depends on unexplained details of the judges' behaviour. If the judges cannot tell the difference between the formulas (but are forced to give an answer anyway), then they are equally likely to choose any glass,* and so there is a 2/3 chance that a judge will choose B. If the judges can tell the difference, and realise they have been given two glasses of B and one of A, but find both equally attractive, then arguably they are likely to choose randomly between A and B, so there is a 1/2 chance that a judge will choose B.

*I'm assuming the glasses are not labelled "A" and "B".

(To literally answer your question, you tell if a judge states a preference for formula B by asking him and listening to his answer. However, I suppose that is not what you are really asking.)

[Isbell]

Hi Dozy, how are you doing lately? For some reason I know that you've been inactive for quite awhile back. Whatever it is, I hope everything is GOOD with you now.

I particularly like your explanation (without a doubt) and I'm more inclined to believe the latter is true.

Please allow me to say a very heartfelt thanks and also ask another math question.

There are 5 different color balls in a jar. What is the probability that in picking and replacing five balls, that two of them were either green or purple?

I actually mean to ask the probability that will result in the following outcomes:
(Green or purple ball) and (Green or purple ball) and 3 other colored balls

In this case, do you think the question above carries the intended meaning?

Thanks again.

[Dozy]

With questions like this, I think you have to take pains to spell everything out in laborious detail, otherwise it is very easy for ambiguities to creep in. As a first stab, and if I understood correctly, I would suggest something like this:

"A jar contains five balls, each of a different colour, including one green ball and one purple ball. A ball is selected at random, inspected, and then returned to the jar. This procedure is carried out a total of five times. Of the five balls selected, what is the probability that exactly one is green and exactly one is purple?"

[Immimeniasync]

Enjoy, one of my favs ;D
http://bit.ly/xxQSUf

[Isbell]

"A jar contains five balls, each of a different colour, including one green ball and one purple ball. A ball is selected at random, inspected, and then returned to the jar. This procedure is carried out a total of five times. Of the five balls selected, what is the probability that exactly one is green and exactly one is purple?"

Hmm...that is a little off the mark, Dozy. By "There are 5 different color balls in a jar. What is the probability that in picking and replacing five balls, that two of them were either green or purple?" I mean one of the draw could be either a green or a purple ball, and another draw could also be either a green or purple ball, and then the rest of the three draws must be balls of different colors (but not green or purple). This doesn't necessary give us exactly one green and exactly one purple ball combinations of possibilities because if I draw a green ball in one of the draw and another green ball in another draw (where these two draws are bounded with restriction) and I further draw another 3 different colors balls, that would not give us the outcome that exactly one is green and exactly one is purple ball. *Sigh*... I think I've expressed the question badly.

[Dozy]

Oops, apologies, my mistake for not reading your post properly.

Unfortunately, I can't at the moment think of any appealing and succinct way to express the required meaning. I'm not a huge fan of "What is the probability that two of them are either green or purple?". It seems hard to understand. However, more explicit alternatives seem to get very wordy. If you do stick with that wording then I think you should say "exactly two" rather than "two". This is because "two" could be interpreted as "at least two".

If I think of anything better, I will return ... or perhaps another forum member can see a way...

[Alan]

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Hi Isbell,

How about this:

A jar contains five balls, each of a different colour, including one green ball and one purple ball. A ball is selected at random, inspected, and then returned to the jar. This procedure is carried out a total of five times. Of the five balls selected, what is the probability that one will definitely be green and one definitely be purple?

Alan
_________________
English as a Second Language
You can read my ESL story Present Simple

[Dozy]

[Isbell]