Muddy Points

Lesson 2: Introducation to Simulations

Fall 2025

1. I think just clarification on what it means to have “replacement” and “w/o replacement.” I think it means something to do with an event not being replicated while the latter, an event cannot be done twice? Also, what is the importance of replacement.

When we say “with replacement,” it means that after we select an item (like drawing a card from a deck), we put it back before selecting again. This means that the probability of selecting that item remains the same for each draw. For example, if you draw a card from a standard deck of 52 cards and then put it back, the probability of drawing any specific card (like an Ace) remains 1/52 for each draw.

On the other hand, “without replacement” means that once an item is selected, it is not put back. This means that the probability of selecting that item changes for subsequent draws because there are fewer items left to choose from. For example, if you draw a card from a deck and do not put it back, the probability of drawing an Ace on the next draw changes because there are now only 51 cards left in the deck.

It’s less about the importance of replacement, but that we accurately represent whatever scenario we want to simulate!