Sampling with replacement

Sampling with replacement is a method of taking a sample of the population in question. One takes the sample, then replaces the sample back into the population, then draws another sample.

Example

What is the probability of drawing four red cards in a row, with replacement?

Probability of drawing a red card: 26/52, or 1/2.

Probability of drawing four red cards in a row with replacement? 1/2⁴

Sampling without replacement

Sampling without replacement is much the same, except the sample is not returned to the population.

Example

What is the probability of drawing four red cards in a row, without replacement?

Probability of drawing a red card: 26/52

Probability of drawing four red cards? (26/52)*(25/51)*(24/50)*(23/49)

As we removed a card, we didn't replace it, so the population size went down.