Whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, four green ones, three white ones, and one purple one. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. She does not have all the red ones.

0.8586 = 85.86% probability that she does not have all the red ones.

Step-by-step explanation:

The marbles are grabbed without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this question:

Bag has 4 + 4 + 3 + 1 = 12 marbles, which means that

She grabs eight of them, which means that

Four are red, which means that

Probability that she does not have all the red ones.

This is

In which

Then

0.8586 = 85.86% probability that she does not have all the red ones.