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
3
5
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