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, .
- The probability that it is Friday, .
We are asked to find the probability that a student is absent given that it is Friday, .
This is a conditional probability, which can be calculated using the formula:
Substituting the given values:
Thus, the probability that a student is absent given that today is Friday is , or 15%.
Would you like more details on this calculation or have any questions?
Here are some related questions you might want to explore:
- How would the probability change if the student is absent 10% of the time overall?
- What is the probability that it is Friday and the student is present?
- How can you use Bayes' Theorem in this context?
- What if the probability that a student is absent on any day is 0.05?
- 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
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