Sample size, probability

In summary, the question is asking for the minimum number of hats that must be drawn without replacement from a set of 400 hats, where each hat is represented by one of six colors, in order to have a high likelihood of obtaining at least one hat of each color. This likelihood can be quantified by setting a probability threshold, such as P>0.9. A potential approach to solving this problem is to draw the minimum number of hats needed to use up all colors except for yellow, and then add one more hat to ensure that all colors are represented.
  • #1
neutrino71
1
0
In a set of 400 hats, each hat is represented by one of six colors (brown, pink, red, orange, blue, yellow). You may assume that each color is represented rather equally in the 400 hats.
What is the minimum amount of samples we must take to be likely to have a sample which has a hat of every color?
 
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  • #2
"likely" is rather qualitative. If can quantify it, say P>0.9, then an answer can be obtained, although the calculation may be a little messy.
 
  • #3
neutrino: do you have any thoughts about how you might start this problem?
 
  • #4
neutrino71 said:
In a set of 400 hats, each hat is represented by one of six colors (brown, pink, red, orange, blue, yellow). You may assume that each color is represented rather equally in the 400 hats.
What is the minimum amount of samples we must take to be likely to have a sample which has a hat of every color?
what minimum # of hats must be drawn (without replacement) to have probability 1 of having each hat color represented at least once (if each color is "rather equally represented" in the original set of 400 hats)?
(hint: what minimum # must be drawn to use up all colors except yellow, then choose 1 more.)
 

What is sample size?

Sample size refers to the number of observations or data points included in a study or experiment. It is an important factor in determining the accuracy and reliability of the results.

Why is sample size important?

Sample size is important because it affects the precision and generalizability of the results. A larger sample size tends to provide more accurate and reliable results, as it reduces the impact of random variation or chance.

How is sample size determined?

The determination of sample size depends on various factors, such as the research question, the desired level of precision, and the resources available. Generally, a larger sample size is preferred, but it should also be feasible and practical to obtain.

What is probability in relation to sample size?

Probability is the likelihood or chance of a specific outcome or event occurring. In relation to sample size, probability can help determine the likelihood of obtaining a certain result or finding in a study. It can also be used to calculate the margin of error in the results.

How does sample size affect statistical significance?

Statistical significance is the likelihood that the results of a study or experiment are not due to chance. A larger sample size can increase the statistical significance of the results, as it reduces the impact of random variation. However, a small sample size does not necessarily mean that the results are not statistically significant.

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