In a smoking study 15,273 people smoke 21 to 30 cigarettes a day, and 4,715 of them are Japanese American. What is the probability of being Japanese American given that band?

1. The word given reduces the sample space to the 15,273 people smoking 21 to 30 cigarettes a day. 2. Of those, 4,715 are Japanese American. 3. The conditional probability is therefore 4,715 divided by 15,273. 4. Dividing 4,715 by the study total of 100,450 gives the joint probability instead. 5. That joint figure answers the question with and rather than given, which is a different quantity. 6. The count 8,378 belongs to Japanese Americans smoking at most ten cigarettes a day, a different band altogether. _Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 3 "Probability Topics", section 3.5 Venn Diagrams_