To find the probability that an object has exactly two wheels given that the object has wheels, we first need to identify all the vehicles in the sample space that have wheels.
The sample space \( S = { \text{car, train, unicycle, boat, bicycle, tricycle, motorcycle} } \) can be filtered for the vehicles that have wheels:
- Unicycle - 1 wheel
- Bicycle - 2 wheels
- Tricycle - 3 wheels
- Motorcycle - 2 wheels
From this, the vehicles with wheels are:
- Unicycle
- Bicycle
- Tricycle
- Motorcycle
That gives us a total of 4 vehicles with wheels. Now, we need to determine how many of these have exactly 2 wheels:
- Bicycle - 2 wheels
- Motorcycle - 2 wheels
Thus, there are 2 vehicles with exactly 2 wheels.
Now we can calculate the probability:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes with wheels}} = \frac{2}{4} = \frac{1}{2} \]
The probability that an object has exactly two wheels, given that the object has wheels, is \( \frac{1}{2} \). None of the provided response options match this value, suggesting there may be a mistake in the options given or the interpretation of the vehicles in the original sample space.