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, five green ones, four white ones, and three 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

I don't know what example 1 is, thus I don't know how you are taught to do these.

Here is how I would do it
Number of ways to choose 8 from 15 = C(15,8) = 6435

at least one green ---> exclude the case of no green
number with no green = (10,8) = 45
so the number with at least one green = 6435-45 = 6390

prob(of at least one green) = 6390/6435 =142/143

or 1 - 45/6435 = 142/143

To find the probability of the event "she has at least one green one," we can use the concept of complementary events. The complement of "she has at least one green one" is "she has no green ones."

Let's calculate the probability of the complement first:
- Suzan grabs a total of eight marbles from the bag.
- The number of green marbles in the bag is five.
- The probability of Suzan grabbing a non-green marble on the first pick is (12/15) because there are 12 marbles that are not green out of 15 total marbles in the bag.
- Since each marble pick is independent and there are no green marbles in the bag, the probability of Suzan grabbing eight non-green marbles is calculated as follows:
P(no green) = (12/15) x (11/14) x (10/13) x (9/12) x (8/11) x (7/10) x (6/9) x (5/8)

Now, we can find the probability of the event "she has at least one green one" by subtracting the probability of the complement from 1:
P(at least one green) = 1 - P(no green)

Let's calculate the probabilities:

P(no green) = (12/15) x (11/14) x (10/13) x (9/12) x (8/11) x (7/10) x (6/9) x (5/8)
= 0.2520

P(at least one green) = 1 - P(no green)
= 1 - 0.2520
= 0.7480

Therefore, the probability of the event "she has at least one green one" is 0.7480, which can be expressed as a fraction in lowest terms as 187/250.

To find the probability of Suzan grabbing at least one green marble out of eight marbles, we need to calculate the probability of the complement event and subtract it from 1.

First, let's find the probability that Suzan doesn't grab any green marbles out of the eight she picks.

The total number of marbles in the bag is 3 (red) + 5 (green) + 4 (white) + 3 (purple) = 15.

The number of ways for Suzan to choose eight marbles without any green ones is the number of ways to choose all eight marbles from the remaining 15 non-green marbles. This is given by the combination formula:

C(15, 8) = 15! / (8! * (15-8)!) = 6435.

The total number of ways for Suzan to choose any eight marbles from the bag is given by:

C(15, 8) = 15! / (8! * (15-8)!) = 6435.

Now, the probability of Suzan not grabbing any green marbles is:

P(no green) = (number of ways to choose no green marbles) / (total number of ways to choose any eight marbles)
= 6435 / 6435
= 1.

Since we want to find the probability of the complement event (Suzan grabbing at least one green marble), we subtract the probability of not grabbing any green marbles from 1:

P(at least one green) = 1 - P(no green)
= 1 - 1
= 0.

So, the probability of Suzan grabbing at least one green marble out of the eight she picks is 0.

Therefore, the probability can be expressed as the fraction 0/1, which is already in its lowest terms.