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Among 130 musicians, 72 are female, 62 studied in school and 38 are both. Are being female and learning in school independent?
AYes, because 0.29 rounds down to 0.26
BNo, because 0.29 does not equal 0.26
CYes, because 0.29 is larger than 0.26
DNo, because 72 does not equal 62 here
Answer & Solution
Correct answer: B. No, because 0.29 does not equal 0.26
1. The joint probability is 38 divided by 130, which is 0.29.
2. The probability of being female is 72 divided by 130, which is about 0.55.
3. The probability of learning in school is 62 divided by 130, which is about 0.48.
4. Multiplying those two gives about 0.26.
5. Since 0.29 does not equal 0.26, the two events are not independent.
6. Rounding one figure to match the other is not a test, and comparing the raw counts 72 and 62 tests nothing at all.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.5 Venn Diagrams_
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