To find the probability that both marbles drawn from the jar are green, we can use the concept of conditional probability.
There are a total of 18 marbles, and out of those, 7 are green.
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The probability that the first marble drawn is green: \[ P(\text{First is green}) = \frac{7}{18} \]
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If the first marble drawn is green, there will be 6 green marbles left in the jar out of a total of 17 marbles (since one has been removed). The probability that the second marble drawn is green given that the first was green: \[ P(\text{Second is green | First is green}) = \frac{6}{17} \]
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The overall probability that both marbles drawn are green is the product of the two probabilities: \[ P(\text{Both are green}) = P(\text{First is green}) \times P(\text{Second is green | First is green}) = \frac{7}{18} \times \frac{6}{17} \]
Calculating this: \[ P(\text{Both are green}) = \frac{7 \times 6}{18 \times 17} = \frac{42}{306} \]
Thus, the probability that both marbles drawn are green is: \[ \frac{42}{306} \]
This is the final answer, and you do not need to simplify it.