A group of students were surveyed to see if they were enrolled in a music or art course. The results are shown in the table below.
Music= 15 Students                               Art= 20 Students
Both Music and Art= 5 Students               Neither= 50 Students
What is the probability that a randomly chosen student is taking a music course, if they are taking an art course?

To find the probability that a randomly chosen student is taking a music course, given that they are taking an art course, we can use conditional probability.

### Step 1: Identify the relevant numbers
- Total number of students taking Art = 20
- Number of students taking both Music and Art = 5

### Step 2: Apply the formula for conditional probability
The conditional probability \( P(Music \mid Art) \) is given by:

\[
P(Music \mid Art) = \frac{\text{Number of students taking both Music and Art}}{\text{Total number of students taking Art}}
\]

### Step 3: Substitute the values
\[
P(Music \mid Art) = \frac{5}{20} = \frac{1}{4}
\]

### Final Answer:
The probability that a randomly chosen student is taking a music course, given that they are taking an art course, is \(\frac{1}{4}\) or 0.25.

Would you like more details, or do you have any other questions?

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Here are 5 related questions:
1. What is the probability that a student is enrolled in both Music and Art?
2. How would you find the probability of a student taking Music if not taking Art?
3. What is the probability that a randomly selected student is taking at least one of the courses?
4. How would the probability change if the number of students taking both Music and Art increased to 10?
5. What is the total number of students surveyed?

**Tip:** Conditional probability is a powerful tool in determining how likely an event is, given that another event has occurred. It's especially useful when analyzing dependencies between different events.

Explore how to find the probability that a randomly chosen student is taking a music course, given that they are enrolled in an art course. Learn the application of conditional probability using specific data points from a student survey. Suitable for high school students studying probability and statistics.

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