Question

You randomly draw a marbles out of a bag containing 4 green marbles, 6 blue marbles, 8 yellow marbles, and 2 red marbles. Find the probability of drawing a green marble, replacing it then drawing a yellow marble.

Answer 1

Let's solve this problem step by step.

First, let's determine the total number of marbles in the bag. We'll add up all the marbles of each color:

- Green marbles: 4
- Blue marbles: 6
- Yellow marbles: 8
- Red marbles: 2

The total number of marbles is:

\( Total\ marbles = Green\ marbles + Blue\ marbles + Yellow\ marbles + Red\ marbles \)

\( Total\ marbles = 4 + 6 + 8 + 2 \)

\( Total\ marbles = 20 \)

Now, the probability of drawing any specific marble color is the number of that color of marbles divided by the total number of marbles.

For the first part of the problem:

1. Drawing a green marble:

The probability of drawing a green marble (\( P_{\text{green}} \)) is the number of green marbles divided by the total number of marbles.

\( P_{\text{green}} = \frac{4}{20} = \frac{1}{5} \)

You then put the green marble you drew back in the bag. This means the total number of marbles in the bag remains unchanged.

2. Drawing a yellow marble afterwards:

Now let's calculate the probability of drawing a yellow marble after replacing the green marble. Since the marbles were replaced, the total stays at 20, and the probability of drawing a yellow marble (\( P_{\text{yellow}} \)) is again the number of yellow marbles divided by the total number of marbles.

\( P_{\text{yellow}} = \frac{8}{20} = \frac{2}{5} \)

3. Combine the probabilities:

Since you replace the green marble before drawing the yellow marble, these two events are independent. To find the probability of both independent events occurring (\( P_{\text{green and yellow}} \)), you multiply the probability of each individual event happening.

\( P_{\text{green and yellow}} = P_{\text{green}} \times P_{\text{yellow}} \)

\( P_{\text{green and yellow}} = \frac{1}{5} \times \frac{2}{5} \)

\( P_{\text{green and yellow}} = \frac{2}{25} \)

So the probability of drawing a green marble first and then drawing a yellow marble after replacing the green marble back into the bag is \( \frac{2}{25} \) or 8%.

Answer 2

2/25

Explanation:

4 green marbles, 6 blue marbles, 8 yellow marbles, and 2 red marbles. = 20 marbles

P( green) = green/total = 4/20 = 1/5

Replace the marble

4 green marbles, 6 blue marbles, 8 yellow marbles, and 2 red marbles. = 20 marbles

P(yellow) = yellow/total = 8/20 = 2/5

P(green, replace, yellow) = 1/5*2/5 = 2/25