The probability that it is Friday and that a student is absent is 0.03. Since there are 5 school days in a week, the probability that it is Friday is 0.2. What is the probability that a student is absent given that today is Friday?

We are given the following information:

- The probability that it is Friday and the student is absent, \( P(\text{Friday and Absent}) = 0.03 \).
- The probability that it is Friday, \( P(\text{Friday}) = 0.2 \).

We are asked to find the probability that a student is absent given that it is Friday, \( P(\text{Absent} \mid \text{Friday}) \).

This is a conditional probability, which can be calculated using the formula:

\[
P(\text{Absent} \mid \text{Friday}) = \frac{P(\text{Friday and Absent})}{P(\text{Friday})}
\]

Substituting the given values:

\[
P(\text{Absent} \mid \text{Friday}) = \frac{0.03}{0.2} = 0.15
\]

Thus, the probability that a student is absent given that today is Friday is \( 0.15 \), or 15%.

Would you like more details on this calculation or have any questions?

Here are some related questions you might want to explore:

1. How would the probability change if the student is absent 10% of the time overall?
2. What is the probability that it is Friday and the student is present?
3. How can you use Bayes' Theorem in this context?
4. What if the probability that a student is absent on any day is 0.05?
5. How can the complement rule help calculate the probability of a student being present?

**Tip:** Conditional probability helps you update predictions when new information is provided. It's essential in many real-world decision-making scenarios.

Understand how to calculate the conditional probability that a student is absent given that it is Friday. This example walks through a step-by-step solution using the formula P(Absent | Friday) = P(Friday and Absent) / P(Friday) with specific values, making it ideal for Grades 10-12 students.

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