Math Problem Statement
Solution
Problem Analysis
The question asks for the probability that a randomly selected student is taking math, science, or both. This requires calculating the union of two sets: (students taking math) and (students taking science). The formula for the union of two sets is:
Given Information:
- Total students:
- Students taking math ():
- Students taking science ():
- Students taking both math and science ():
Calculation:
We need to calculate , the probability of a student being in at least one of the sets (math, science, or both). Using the formula:
Substitute the values:
Step-by-step Computation:
Final Answer:
Would you like further explanation or additional details?
Related Questions:
- How do you calculate the probability of the intersection of two sets ()?
- What is the probability that a randomly selected student is taking only math?
- What is the probability that a student is taking only science?
- If a student is known to be taking math, what is the probability they are also taking science?
- How would the result change if the total number of students was different?
Tip:
When dealing with union and intersection in probability, always ensure you account for overlapping elements to avoid double-counting!
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Math Problem Analysis
Mathematical Concepts
Probability
Set Theory
Union of Sets
Formulas
P(M ∪ S) = P(M) + P(S) - P(M ∩ S)
Theorems
Basic Probability Theorem
Suitable Grade Level
Grades 9-12
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