# Probability » Combinations with and without replacing

With some exercises you have a combination between with and without replacing. Often you use the vase model to calculate the probability and then you use this probability in the product rule.

*Example*

In a vase are 5 red, 4 white and 3 blue marbles.

John takes 3 marbles in one grab without looking and afterwards replaces these.

He repeats this another 5 times.

Calculate the probability that he had exactly two grabs without a red marble.

Answer

The answer can be found by doing the following two steps:

First calculate the probability of grabbing no red marble using the vase model.

7

35

0

12

3 ≈ 0.159

After that you calculate the probability of having exactly 2 times not a red marble after 6 grabs. The probability of getting a red marble is 1 – 0.159 = 0.841.

6

2(0.159)^{2}(0.841)^{4} ≈ 0.19