Question

A sample of two items is selected without replacement from a batch. Describe the (ordered) following batches

of the
a)sample space for each The batch contains the items {a, b, g}
b)The batch contains 4 defective items and 15 good items
and 10 mediocre items.

Answer 1

The question pertains to the sample space of selecting items without replacement, involving both a simple batch of three distinct items and a batch with a mixture of items. For the first batch, the sample space is the possible ordered pairs, and for the larger batch of mixed quality items, it includes all possible ordered pairs without repetition.

Step-by-step explanation:

The concept being addressed in the student's question is sampling from a finite population without replacement, which is a principle in probability and statistics. In such scenarios, the sample space consists of all possible outcomes of selecting items from the batch, considering the order in which they are selected. For each batch described, we can detail the sample space as follows:

• For the batch containing items {a, b, g}, the sample space of selecting two items without replacement is {ab, ag, ba, bg, ga, gb}.
• For the batch with 4 defective, 15 good, and 10 mediocre items, since we're dealing with a large batch and the question only asked for the description of sample space for each batch and not probabilities, it's sufficient to say that the sample space consists of all possible ordered pairs of these items, which could be defective-defective, defective-good, defective-mediocre, good-good, good-mediocre, mediocre-mediocre, and so on, without reusing any individual item.

When dealing with hypergeometric distribution, which emerges from scenarios like the second batch, we typically consider the probability of getting a certain number of items from the group of interest, without replacement from the combined group.