Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, three green ones, four white ones, and two purple ones. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.] She has all the red ones.

The probability of the Suzan choosing all red marbles at once  expressing it as a fraction in lowest terms = 14/143

Suzan has a bag containing marbles

The Number of green marbles in the bag = 3

The Number of red  marbles in the bag = 4

The Number of white marbles in the bag = 4

The Number of purple marbles in the bag = 2

Total number of marbles = 3+ 4 + 4+ 2 = 13  

The total 8 number of marbles selected at random

To find

The probability of choosing all red marbles at once

Number of ways to choose 8 marbles out of 13 marbles =

Number of ways of choosing 4 red marbles out of 4 marbles =

Number of ways of choosing 4 non  red  marbles out of  9 marbles =

So the total number of marbles

Probability = P = () /   =  (1 126)/1287 = 0.097902098 = 14/143

The probability of the Suzan choosing all red marbles at once  expressing it as a fraction in lowest terms = 14/143

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14 / 143

Step-by-step explanation:

There are a total of 4+3+4+2=13 marbles.

There are ₄C₄ ways to choose 4 red marbles from a group of 4.

There are ₉C₄ ways to choose 4 non-red marbles from a group of 9.

There are ₁₃C₈ ways to choose 8 marbles from a group of 13.

So the probability is:

P = ₄C₄ × ₉C₄ / ₁₃C₈

P = 1 × 126 / 1287

P = 14 / 143

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step-by-step explanation: