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:

= \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? --- 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.