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Let's break down the problem based on the table shown in the image and calculate the requested probabilities.

The table provides the following dataLet's break down the problem based on the table shown in the image and calculate the requested probabilities.

The table provides the following 

|          | Black | Green | Blue | Total |
|----------|-------|-------|------|-------|
| **Hybrid** | 37    | 28    | 39   | 104   |
| **Standard** | 66    | 42    | 59   | 167   |
| **Total** | 103   | 70    | 98   | 271   |

### Question A: \( P(\text{Standard}) \)

The probability of selecting a car with a Standard engine is the total number of Standard cars divided by the total number of cars.

\[
P(\text{Standard}) = \frac{\text{Number of Standard cars}}{\text{Total number of cars}} = \frac{167}{271}
\]

### Question B: \( P(\text{Blue}) \)

The probability of selecting a Blue car is the total number of Blue cars divided by the total number of cars.

\[
P(\text{Blue}) = \frac{\text{Number of Blue cars}}{\text{Total number of cars}} = \frac{98}{271}
\]

### Question C: \( P(\text{Hybrid} \mid \text{Blue}) \)

This is the conditional probability of the car being a Hybrid given that it is Blue. This is calculated as the number of Hybrid Blue cars divided by the total number of Blue cars.

\[
P(\text{Hybrid} \mid \text{Blue}) = \frac{\text{Number of Hybrid Blue cars}}{\text{Total number of Blue cars}} = \frac{39}{98}
\]

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Let me know if you want more details on these calculations, or if you have any further questions!

Here are 5 related questions to consider:
1. How do we calculate conditional probability in general?
2. What is the probability of selecting a Hybrid car?
3. How would you calculate the probability of selecting a Green Standard car?
4. Can you calculate \( P(\text{Blue} \mid \text{Hybrid}) \)?
5. How can the probabilities in the table be visualized using a bar chart?

**Tip:** Always make sure the sum of probabilities for all outcomes equals 1 to ensure correctness!

The featured car at the auto dealership comes in three colors: Black, Green, or Blue, and comes with either a Hybrid or Standard engine. The monthly sales of the featured car are shown in the table below. Calculate the following probabilities: P(Standard), P(Blue), P(Hybrid GIVEN Blue).

Learn how to calculate probabilities using a two-way table. This problem covers finding the probability of selecting a Standard engine car, a Blue car, and the conditional probability of selecting a Hybrid car given it is Blue. Includes detailed step-by-step solutions.

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