Probability and Stats - Show the Sample Space

In summary, the sample space for observing items on an assembly line until both good and not good items are observed is represented by the set S = {GN, GGN, GG...N, GG..., NG, NNG, NN...G, NN...}.
  • #1
Of Mike and Men
54
3

Homework Statement



An assembly line is observed until items of both types—good (G) items and items not meeting specification (N)—are observed. Show the sample space.

Homework Equations


Let G be Good
Let N be Not Good

The Attempt at a Solution


S = {GN, GGN, GG...N, GG..., NG, NNG, NN...G, NN...}

I'm not sure if this represents the sample space. I realize the sample space is essentially infinite, but I'm not sure if I've accomplished the task of showing the sample space. I also am not sure if I am missing anything or misunderstanding the question.

Thanks.
 
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  • #2
Of Mike and Men said:

Homework Statement



An assembly line is observed until items of both types—good (G) items and items not meeting specification (N)—are observed. Show the sample space.

Homework Equations


Let G be Good
Let N be Not Good

The Attempt at a Solution


S = {GN, GGN, GG...N, GG..., NG, NNG, NN...G, NN...}

I'm not sure if this represents the sample space. I realize the sample space is essentially infinite, but I'm not sure if I've accomplished the task of showing the sample space. I also am not sure if I am missing anything or misunderstanding the question.

Thanks.

Yes, that is the sample space.
 

Related to Probability and Stats - Show the Sample Space

1. What is the sample space in probability and statistics?

The sample space in probability and statistics refers to the set of all possible outcomes or events that can occur in a given experiment or situation. It is denoted by the symbol Ω and is an important concept used to calculate probabilities.

2. What is the difference between a sample space and an event in probability and statistics?

The sample space is the set of all possible outcomes, while an event is a subset of the sample space that represents a specific outcome or combination of outcomes. In other words, the sample space is the complete set of all possibilities, while an event is a specific occurrence within that set.

3. How do you determine the size of a sample space?

The size of a sample space is determined by counting the number of possible outcomes or events. For example, if you are rolling a six-sided die, the sample space would have six possible outcomes (1,2,3,4,5,6).

4. Can the sample space change in different situations?

Yes, the sample space can change depending on the situation or experiment being conducted. For example, if you are flipping a coin, the sample space would be {heads, tails}, but if you are rolling a pair of dice, the sample space would be {2,3,4,5,6,7,8,9,10,11,12}.

5. How is the sample space used in calculating probabilities?

The sample space is used to determine the total number of possible outcomes, which is then used to calculate the probability of a specific event occurring. The probability of an event is equal to the number of favorable outcomes divided by the total number of possible outcomes in the sample space.

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