In a population problem, 40% buy iPods and 35% of those enjoy country music. If N people are in the group, how many will enjoy country music on their iPods?

In a population problem, 40% buy iPods and 35% of those enjoy country music. If N people are in the group, how many will enjoy country music on their iPods?

• A. 0.14N
• B. 0.05N
• C. 0.25N
• D. 0.35N

Answer: (A)

Think in terms of the overlap of two events. You want the fraction of the whole group that both buys iPods and enjoys country music. Start with the fraction that buy iPods: 0.40. Of those, the fraction that enjoys country music is 0.35. Multiply to get the joint fraction: 0.40 × 0.35 = 0.14. So among N people, the number who enjoy country music on their iPods is 0.14N. The other options would represent different quantities (for example, all country music fans regardless of iPod ownership), not the subset that both buys iPods and enjoys country music.

Think in terms of the overlap of two events. You want the fraction of the whole group that both buys iPods and enjoys country music. Start with the fraction that buy iPods: 0.40. Of those, the fraction that enjoys country music is 0.35. Multiply to get the joint fraction: 0.40 × 0.35 = 0.14. So among N people, the number who enjoy country music on their iPods is 0.14N. The other options would represent different quantities (for example, all country music fans regardless of iPod ownership), not the subset that both buys iPods and enjoys country music.