Work out the probability that this person does not have brown eyes given that they have fair hair.

      Give your answer as a fraction in its simplest form as a/b where a and b are whole numbers.

To solve this problem, we need to find the probability that a person does not have brown eyes given that they have fair hair.

### Step 1: Total number of people with fair hair

First, find the total number of people with fair hair:

\[
\text{Total number of people with fair hair} = 8 + 7 = 15
\]

### Step 2: Number of people with other eye colors and fair hair

Next, find the number of people with other eye colors (i.e., not brown) and fair hair:

\[
\text{Number of people with other eye colors and fair hair} = 7
\]

### Step 3: Probability calculation

Now, calculate the probability that a person does not have brown eyes given that they have fair hair:

\[
\text{Probability of not having brown eyes given fair hair} = \frac{7}{15}
\]

### Final Answer

The probability that a person does not have brown eyes given that they have fair hair is \(\frac{7}{15}\).

Do you want more details or have any questions?

Here are 8 additional questions related to this topic:

1. What is the probability that a person has other eye colors given that they have dark hair?
2. How would the probabilities change if more people with other eye colors and fair hair were added?
3. What is the probability that a person has fair hair given that they do not have brown eyes?
4. How would you calculate the probability of someone having brown eyes given that they have fair hair?
5. What is the probability of a person having brown eyes and dark hair?
6. If a person has other eye colors, what is the probability that they have fair hair?
7. What is the probability of a person not having dark hair given that they have brown eyes?
8. How would the result change if more people with brown eyes and fair hair were added?

**Tip:** Conditional probability requires careful consideration of the given condition; always ensure that the total under the condition is correctly identified.

Learn how to calculate the probability that a person does not have brown eyes given that they have fair hair. This problem involves conditional probability and is solved step-by-step with clear explanations. Suitable for students in Grades 9-12.

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