Question

Explain the difference between with replacement and without replacement in probability.

Answer 1

The difference between replacement and without replacement in probability is that replacement means an item is put back into the population after being chosen, making selections independent; without replacement means items are not put back, making selections dependent.

Step-by-step explanation:

The concept of with replacement vs. without replacement is crucial in understanding different probabilities in sampling. When you sample with replacement, each selection is returned to the population before the next one is made. This means the probability remains unchanged each time, and the events are considered independent. An example is picking a card from a deck, replacing it, then picking another card.

Conversely, when you sample without replacement, once an item is selected, it is not returned to the population. This causes the probability to change for subsequent selections, making the events dependent. An example of this would be picking a card from a deck and keeping it out before picking the next one. The chance of the next card being of a certain rank is now different.

Answer 2

With replacement means the same item can be chosen more than once. Without replacement means the same item cannot be selected more than once.