# Statistics Probability Question

## Homework Statement

1. The manufacturer of a low-calorie dairy drink wishes to compare the taste appeal of a new formula (formula B) with that of the standard formula (formula A). Each of 3 judges is given 3 glasses in random order, two containing formula A and the other containing formula B. Each judge is asked to state which glass he most enjoyed. Suppose that two formulas are equally attractive. Let X be the number of judges stating a preference for the standard formula (A).
a) List all the elements of the sample space (S)
b) Find the probability distribution for a random variable X
c) What is the probability that at least 2 of the judges state a preference for formula A
d) Find the expected value of a random variable X
e) Find the standard deviation of random variable X

0=P(X)=1
Σ P(X)=1
E(X)= Σx P(X)

## The Attempt at a Solution

3. I don't really know where to start for this one. I know that each judge has a 2/3 chance of getting formula A and there are 3 judges. I'm confused at how you make the probability distribution for this problem.

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LCKurtz
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You start by answering part (a). If X is the number of judges favoring A what is the sample space for X? X could be .....?

You start by answering part (a). If X is the number of judges favoring A what is the sample space for X? X could be .....?
So then X could be 0,1,2,3 right?

LCKurtz
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So then X could be 0,1,2,3 right?
Yes. If you consider it a "success" if a judge picks A then X counts the number of "successes". Does that ring any bells? Can you calculate P(X=0) directly?

Yes. If you consider it a "success" if a judge picks A then X counts the number of "successes". Does that ring any bells? Can you calculate P(X=0) directly?
So then the probability of there being 0 success would be 1/3 right?

LCKurtz
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So then the probability of there being 0 success would be 1/3 right?
No. For X = 0, all three judges must pick B.

As an aside, what discrete probability distributions have you studied?

No. For X = 0, all three judges must pick B.

As an aside, what discrete probability distributions have you studied?
We just started them last week. What do you mean by "what" discrete probability? There are different kinds?

LCKurtz
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Gold Member
No. For X = 0, all three judges must pick B.

As an aside, what discrete probability distributions have you studied?
We just started them last week. What do you mean by "what" discrete probability? There are different kinds?
I didn't ask you "what discrete probability". I asked "what discrete probability distributions". Names like Binomial, Geometric, and others. Have you talked about the Binomal distribution yet?

I asked because I didn't know what level your course was or what you have had. If you haven't had the various standard probability distributions yet, you can still answer your question by calculating the probabilities directly.

For example, the only way X = 0 is possible if all three independent judges choose B, and for each one the probability of them doing that is 1/3. So what's the probability they all three do it?

I didn't ask you "what discrete probability". I asked "what discrete probability distributions". Names like Binomial, Geometric, and others. Have you talked about the Binomal distribution yet?

I asked because I didn't know what level your course was or what you have had. If you haven't had the various standard probability distributions yet, you can still answer your question by calculating the probabilities directly.

For example, the only way X = 0 is possible if all three independent judges choose B, and for each one the probability of them doing that is 1/3. So what's the probability they all three do it?
Binomial doesn't sound familiar to me. The problems we've done so far in class are when we set up a table with X and the P(X) where they give us the X values and then you plug them into the P(X). That's why I'm confused with this problem trying to get all of the X's on my own instead of them being given to us already.

To illustrate the type of table i'm talking about, its exactly like this one.

LCKurtz
Homework Helper
Gold Member
If you haven't had the various standard probability distributions yet, you can still answer your question by calculating the probabilities directly.

For example, the only way X = 0 is possible if all three independent judges choose B, and for each one the probability of them doing that is 1/3. So what's the probability they all three do it?
Binomial doesn't sound familiar to me. The problems we've done so far in class are when we set up a table with X and the P(X) where they give us the X values and then you plug them into the P(X)....
Which is exactly what I was getting at when I gave you that "for example" above, which you ignored.

Which is exactly what I was getting at when I gave you that "for example" above, which you ignored.
Which I ignored? Relax. I didn't understand what you were saying so I showed you a picture of the table that looked most familiar to what we have been doing in class.