Does this problem make sense? (Probability and Survey Sampling)

In summary, the conversation is about a question for an assignment that the person is having trouble understanding. The question involves selecting elements with certain probabilities and the person is confused about how to calculate the probabilities for the second, third, fourth, and fifth picks. They have noticed that the sum of these probabilities is greater than one, and they are seeking help to understand the problem. A possible solution is suggested in the conversation.
  • #1
gjones89
5
0
Hi,

I am trying to answer a question for an assignment, but am convinced that it doesn't make sense. Please see here: http://img813.imageshack.us/img813/1585/qst.png

My problem is with Plan 2 in the question. The probability of selecting any of the 5 elements on the first selection is 1/5. So for example, I can select element 1 with probability 1/5 on the first pick. But then, how can I work out the probabilities of choosing the 2nd, 3rd, 4th and 5th elements on the 2nd pick? Obviously these probabilities can't just be the numbers in the last column in the table, because if I add together the probabilties for choosing elements 2, 3, 4, and 5 (ignoring row 1 because we are sampling without replacement), I get (1/4 + 1/2 + 1/5 + 7/40) = 9/8, i.e. a total greater than one!

What is going on here? I want to work out the probability of picking, for example, element 1 on the first pick and element 2 on the second pick. Can anyone help?

Thanks.
 
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  • #2
If I understand problem correctly then
P(S[2]=i)=P(S[2]=i|S[1][tex]\neq[/tex]i)*P(S[1][tex]\neq[/tex]i)

so for i=1 then

P(S[2]=1)=(1/8)*(4/5)


will be the same method for other elements
 

1. What is the purpose of asking if a problem makes sense in probability and survey sampling?

Asking if a problem makes sense is important in probability and survey sampling because it helps ensure that the data being collected and analyzed is accurate and relevant. It also helps identify any potential biases or errors that may affect the results.

2. How do you determine if a problem makes sense in probability?

In probability, a problem can be considered to make sense if it follows the basic principles and rules of probability. This includes identifying all possible outcomes, assigning appropriate probabilities to each outcome, and ensuring that the total sum of probabilities is equal to 1.

3. What factors should be considered when evaluating if a problem makes sense in survey sampling?

When evaluating if a problem makes sense in survey sampling, factors such as the sample size, sampling method, and representativeness of the sample should be considered. It is also important to consider any potential biases in the survey design or data collection process.

4. Can a problem still make sense even if the results are unexpected or counterintuitive?

Yes, a problem can still make sense even if the results are unexpected or counterintuitive. This is because probability and survey sampling involve analyzing data and making inferences based on statistical methods, which may sometimes lead to unexpected results. It is important to carefully evaluate and interpret the data to understand the reasoning behind the results.

5. How can asking if a problem makes sense improve the accuracy of the results?

Asking if a problem makes sense can improve the accuracy of the results by helping to identify any potential errors or biases in the data. It also allows for a critical evaluation of the problem and the data collection process, which can lead to more accurate and reliable results.

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