Question

1. lauren has a bag containing 6 red, 8 blue, 5 green, 9 yellow, and 2 white marbles that are all the same size and shape. what is the probability of randomly choosing a white marble on the first pick, not replacing it, and then randomly choosing a green marble on the second pick?

Explanation:

Step1: Calculate total marbles initially

First, find the total number of marbles. Add the number of each color: \(6 + 8 + 5 + 9 + 2 = 30\) marbles.

Step2: Probability of white first

The number of white marbles is 2. So the probability of choosing a white marble first is \(\frac{2}{30}\). After removing one white marble, the total number of marbles becomes \(30 - 1 = 29\).

Step3: Probability of green second

The number of green marbles is 5. So the probability of choosing a green marble second (after removing a white) is \(\frac{5}{29}\).

Step4: Multiply the probabilities

Since these are dependent events (not replacing the first marble), we multiply the two probabilities: \(\frac{2}{30} \times \frac{5}{29} = \frac{10}{870} = \frac{1}{87}\)

Answer:

\(\frac{1}{87}\)