Suppose a jar contains 12 yellow marbles and 28 green marbles. If you reach in the jar and randomly pull out 2 marbles successively (without replacement), find the probability that both are green.
Give your answer as a fraction, or round your answer to 3 places after the decimal point, if necessary.

To find the probability that both marbles drawn are green, we need to calculate it step by step.

### Step 1: Total number of marbles
The total number of marbles in the jar is:
\[
12 \text{ (yellow)} + 28 \text{ (green)} = 40 \text{ marbles}
\]

### Step 2: Probability of drawing a green marble on the first draw
There are 28 green marbles out of 40 total marbles. So, the probability of drawing a green marble on the first draw is:
\[
P(\text{Green on first draw}) = \frac{28}{40} = \frac{7}{10}
\]

### Step 3: Probability of drawing a green marble on the second draw
Since you are not replacing the first marble, there are now 39 marbles left, and only 27 of them are green. So, the probability of drawing a green marble on the second draw, given that the first marble was green, is:
\[
P(\text{Green on second draw}) = \frac{27}{39} = \frac{9}{13}
\]

### Step 4: Multiply the probabilities
Since the two events are dependent (without replacement), we multiply the probabilities:
\[
P(\text{Both green}) = P(\text{Green on first draw}) \times P(\text{Green on second draw})
= \frac{7}{10} \times \frac{9}{13} = \frac{63}{130}
\]

### Final Answer
The probability that both marbles drawn are green is:
\[
\frac{63}{130}
\]

If you want to round this to three decimal places, it is approximately:
\[
0.485
\]

Would you like more details on any step?

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Here are some related questions:
1. What is the probability of drawing two yellow marbles?
2. What is the probability of drawing one green and one yellow marble?
3. How does the probability change if you draw with replacement?
4. What if the jar had 15 yellow and 25 green marbles?
5. How does probability change with three draws instead of two?

**Tip**: When working with probabilities without replacement, remember that the total number of items decreases with each draw.

Suppose a jar contains 12 yellow marbles and 28 green marbles. If you reach in the jar and randomly pull out 2 marbles successively (without replacement), find the probability that both are green. Give your answer as a fraction, or round your answer to 3 places after the decimal point, if necessary.

Find out how to calculate the probability of drawing two green marbles from a jar containing 12 yellow and 28 green marbles, with step-by-step explanations. Learn about dependent events and how to multiply probabilities to get a final answer of 63/130 or approximately 0.485. Suitable for students in Grades 8-10.

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