Question

1. Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing three red marbles, two green ones, five white ones, and one purple one. She grabs seven 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. 

2. 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 at least one green one.

3.  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, two white ones, and three purple ones. She grabs five of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.] 

She has two red ones and one of each of the other colors.

Answer 1

1) Probability = (3C3 * 8C4)/11C7

                     = 70/330 = 7/33

2) Probability = (3C1 * 10C7 + 3C2 * 10C6 + 3C3 * 10C5)/13C8

                      = 1242/1287 = 138/143

3) Probability = (4C2 * 3C1 * 2C1 * 3C1)/12C5

                      = 108/792 = 3/22