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Of 100 hikers, 45 are female, 34 prefer the coastline and 18 are both. Are being female and preferring the coastline independent?
AYes, because 0.18 is greater than 0.153
BNo, because 0.18 does not equal 0.153
CYes, because 0.45 times 0.34 gives 0.18
DNo, because 0.45 does not equal 0.34
Answer & Solution
Correct answer: B. No, because 0.18 does not equal 0.153
1. The joint probability is 18 divided by 100, which is 0.18.
2. The probability of being female is 45 divided by 100, which is 0.45.
3. The probability of preferring the coastline is 34 divided by 100, which is 0.34.
4. Multiplying those two gives 0.153.
5. Since 0.18 does not equal 0.153, the two events are not independent.
6. Comparing 0.45 with 0.34 tests nothing, because independence compares the joint probability with the product.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.4 Contingency Tables and Probability Trees_
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