## What Is Probability Without Replacement Or Dependent Probability?

In some experiments, the sample space may change for the different events. For example, a marble may be taken from a bag with 20 marbles and then a second marble is taken **without replacing** the first marble. The sample space for the second event is then 19 marbles instead of 20 marbles.

This is called probability without replacement or dependent probability. We can use a tree diagram to help us find the probability without replacement.

"Without **replacement**" means that you don't put the ball or balls back in the box so that the number of balls in the box gets less as each ball is removed. This changes the probabilities. Let's look at question 4 above.

What is the probability that if a ball or balls are randomly selected that we choose:

a blue and green ball?

The probability of choosing the blue ball is 2/10 and the probability of choosing the green ball is 3/9 because after the first ball is taken out, there are 9 balls remaining. So the probability is:

2/10 x 3/9 = 6/90 or 1/15 = 6.7% (Compare that with replacement of 6/100 or 6%)

## What does probability without replacement mean?

Sampling **without Replacement** is a way to figure out **probability without replacement**. In other words, you don't **replace** the first item you choose before you choose a second. This dramatically changes the odds of choosing sample items.

## How To Find The Probability Without Replacement Or Dependent Probability?

**Step 1:** Draw the Probability Tree Diagram and write the probability of each branch. (Remember that the objects are not replaced)**Step 2:** Look for all the available paths (or branches) of a particular outcome.**Step 3: **Multiply along the branches and add vertically to find the probability of the outcome.

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