Math Problem Statement

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?

Solution

We are given the following information:

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

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

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

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

Substituting the given values:

P(AbsentFriday)=0.030.2=0.15P(\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 0.150.15, 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.

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Math Problem Analysis

Mathematical Concepts

Probability
Conditional Probability

Formulas

P(Absent | Friday) = P(Friday and Absent) / P(Friday)

Theorems

Conditional Probability

Suitable Grade Level

Grades 10-12