How to find the probability that the next three are not flawed?

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In summary, if you want to know the probability that the next three chosen will be flawless, you need to know the size of the population and the probability that any three chosen are flawed.
  • #1
nontradstuden
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Homework Statement



If you have a sample of size n=20, where X=the number among the n that are flawed=5, how do you go about finding the probability that the next three chosen will be flawless?

do I say (15*14*13*12*11)/ (20*19*18*17*16) .

Or is it (15/20)^5?


How do I go about solving this?
 
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  • #2
nontradstuden said:

Homework Statement



If you have a sample of size n=20, where X=the number among the n that are flawed=5, how do you go about finding the probability that the next three chosen will be flawless?

do I say (15*14*13*12*11)/ (20*19*18*17*16) .

Or is it (15/20)^5?


How do I go about solving this?

I don't understand the question. You say we have 20 items among which 5 are flawed. OK so far? Now you ask about the next three. What does "next" mean here? Do you mean items 21, 22 and 23, or something else? If you mean items 21-23, you need to know something about the probability that a randomly-chosen item is flawed; also, you need to specify the size of the whole population. That is, did we choose 20 from a population of size 24 or size 2400 or size ∞, or what? (It makes a big difference.)

RGV
 
  • #3
If this were "sampling with replacement" or if we were taking sample from a much, much larger "universe", then the probability of any three in a row (or any three) would be the same. But with this problem, the probability the first three will be flawed may be quite different from the probability of the last three. That is why we need to know what you mean by "the next three". Are you assuming that some number have already been chosen?
 
  • #4
Hi folks. Sorry for the late reply.

I really don't know. This question is part three of my problem. I'm supposed to find the Maximum Likelihood estimator of (1-p)^3. I'm told to remember that this is both a probability and a parameter.

I'm confused. The first part asks me to find the Maximum Likelihood Estimator of p for n=20 and X= the number among the n that are flawed. So, I found that to be p-hat= X/n.

This part asks me to find the Maximum Likelihood estimator of (1-p)^3 given n=20 and X=5. Also, to find the probability that the next three are flawless.

This is all I'm given. I don't know where to go with it. I though I would just have to make (1-p) hat= 15/20 and then use sampling without replacement, but I'm grasping at straws.
 
  • #5
I was searching for a way to edit my last response, but I don't see one. anywho, I've solved it. Forgot about assuming independence and the invariance principle. This can be deleted to cyber space because it is not contributing to the site, at all. :/
 

1. What is the formula for calculating the probability of three non-flawed items in a row?

The formula for calculating the probability of three non-flawed items in a row is the product of the individual probabilities. This means that you multiply the probability of the first item being non-flawed by the probability of the second item being non-flawed, and then multiply that by the probability of the third item being non-flawed.

2. How do you determine the individual probabilities of non-flawed items?

The individual probabilities of non-flawed items can be determined by dividing the number of non-flawed items by the total number of items. For example, if there are 10 items in total and 8 of them are non-flawed, then the probability of each individual item being non-flawed is 8/10 or 0.8.

3. Can the probability of three non-flawed items be greater than 1?

No, the probability of three non-flawed items cannot be greater than 1. In probability theory, the maximum value for probability is 1, which represents certainty. This means that the probability of an event occurring is 100%. Anything with a probability greater than 1 is considered impossible.

4. What is the difference between theoretical and experimental probabilities?

Theoretical probability is based on mathematical calculations and assumes that all outcomes are equally likely. Experimental probability, on the other hand, is based on actual data collected from experiments or observations. It may differ from theoretical probability due to chance or other factors that affect the outcome.

5. Can the probability of three non-flawed items be negative?

No, the probability of three non-flawed items cannot be negative. In probability theory, all probabilities are non-negative numbers. Negative probabilities do not make sense in the context of probability, as they would imply that an event has a chance of not occurring, which is impossible.

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