Question

What is the relationship between sampling without replacement and independence and how does that affect the computation of the probabilities of two successive events? How bout sampling with replacement; does that lead to independent or dependent outcomes?

Answer 1

For computing probabilities of two independent evevts which are occuring successively we at first find the probabilities of each of the events separately and then multiply them to get the overall probability.

Sampling without replacement leads to a dependent case beacause the sample which is selected in the first draw has an effect on the sample selected in the second draw.Therefore sampling without replacement leads to dependent outcomes.

Now in sampling with replacement the outcomes are independent. the sample selected in the first draw is again returned and then for the second selection also we obtain the same sample space, that we had in the first draw.