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Selection without Replacement

Just like it sounds, in selection without replacement, you are picking something out of a bag (bucket, hat, any type of container, etc.) and, without putting it back, you pick out a second something.

This means that the total number of objects decreases each time you select without replacement.

Notice how, when we select without replacing, the denominator of the fractions we use to calculate probability change (and get smaller) every time.

(Video) Probability Without Replacement

by Kevin Dorey

Kevin Dorey has a great video explaining probability without replacement. Here is a similar problem to try on your own once you've watched the video.

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Examples: Selecting Without Replacement

Calculating the probability of certain events, we have to consider if we are selecting with or without replacement.

Say we start with a collection of things, selecting with replacement means that each time we take something out, we replace that item with the same thing (or put it back). Selecting without replacement means that each time we take something out, we don't replace it and leave the collection the way it is.

Let's see an example

Let's say you did get a chocolate croissant! You eat your croissant with joy, and now we have these left:

You got lucky and picked a raspberry croissant! We are now left with:

Notice how because we are selecting without replacement, the denominator and numerator both change when we calculate the probability!