Common Core: S-CP.3
Problem 21 of 45s12-021
At a school, 40% of students take Spanish, 20% play in the band, and 10% do both. A student who takes Spanish is chosen at random. What is the probability that the student plays in the band?
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Solution walkthrough1:42
- Draw all students as a square of area 1. Spanish () is of it, and Spanish and band () is .
- Given Spanish: only the Spanish strip counts now. That strip, area , becomes the whole.
- Band inside that strip: .
- Reversed, . That is a different question: it is given band, not Spanish.
- Traps: reverses the condition, forgets to divide, and ignores that the student takes Spanish.