To determine the probability that an object has exactly 2 wheels given that it has wheels, we first identify the objects from the sample space \( S = { \text{car, train, unicycle, boat, bicycle, tricycle, motorcycle} } \) that have wheels and then identify how many of those have exactly 2 wheels.
Step 1: Identify objects with wheels. The vehicles in the sample space that have wheels are:
- Unicycle (1 wheel)
- Bicycle (2 wheels)
- Tricycle (3 wheels)
- Motorcycle (2 wheels)
- Car (4 wheels)
Total objects with wheels:
- Unicycle
- Bicycle
- Tricycle
- Motorcycle
- Car
So, the objects with wheels are: Unicycle, Bicycle, Tricycle, Motorcycle, Car. This gives us a total of 5 objects with wheels.
Step 2: Identify objects with exactly 2 wheels. From the identified objects, the ones that have exactly 2 wheels are:
- Bicycle
- Motorcycle
Total objects with exactly 2 wheels:
- Bicycle
- Motorcycle
So, there are 2 objects with exactly 2 wheels.
Step 3: Calculate the conditional probability. The probability that an object has exactly 2 wheels given that it has wheels can be calculated using the formula:
\[ P(A | B) = \frac{P(A \cap B)}{P(B)} \]
Where:
- \( A \) is the event that the object has exactly 2 wheels.
- \( B \) is the event that the object has wheels.
However, since we have already counted \( A \cap B \) and \( B \), we can simplify as follows:
\[ P(A | B) = \frac{\text{Number of favorable outcomes for A}}{\text{Total outcomes for B}} = \frac{2}{5} \]
Thus, the probability that an object has exactly 2 wheels given that it has wheels is:
\[ \boxed{\frac{2}{5}} \]
2 answers