A bicycle shop rents out bicycles at a park. After lunch, there are 4 black bicycles and 6 silver bicycles remaining to rent. No bicycles are returned and each bicycle is equally likely to be chosen. Which is the probability that the next two bicycles chosen are silver bicycles? ( $$ \frac{1}{5} $$ $$ \frac{1}{3} $$

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To determine the probability that the next two bicycles chosen are both silver, follow these steps:

1. **Total Bicycles Available:**
   - **Black Bicycles:** 4
   - **Silver Bicycles:** 6
   - **Total Bicycles:** 4 + 6 = 10

2. **Probability of Choosing the First Silver Bicycle:**
   $$
   P(\text{First Silver}) = \frac{\text{Number of Silver Bicycles}}{\text{Total Bicycles}} = \frac{6}{10} = \frac{3}{5}
   $$

3. **Probability of Choosing the Second Silver Bicycle (Without Replacement):**
   - After choosing one silver bicycle, there are now 5 silver bicycles left and a total of 9 bicycles.
   $$
   P(\text{Second Silver} \mid \text{First Silver}) = \frac{5}{9}
   $$

4. **Combined Probability:**
   $$
   P(\text{Both Silver}) = P(\text{First Silver}) \times P(\text{Second Silver} \mid \text{First Silver}) = \frac{3}{5} \times \frac{5}{9} = \frac{15}{45} = \frac{1}{3}
   $$

**Final Answer:** $$\boxed{\dfrac{1}{3}}$$
The probability that the next two bicycles chosen are both silver is $$\frac{1}{3}$$.

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