1/5 of the adult population in the U.S. smoked in 2005. Within part of the population that smoked, 6/25 of them were aged 25-44. What fraction of the adult population in the U.S. was aged 25-44 and smoked?

Question

1/5 of the adult population in the U.S. smoked in 2005.  Within part of the population that smoked, 6/25 of them were aged 25-44.  What fraction of the adult population in the U.S. was aged 25-44 and smoked?

anonymous · Answer

P(A and B) = P(A) * P(B | A)
Event A is an adult that smokes.  Event B is an adult that is age 25 - 44.
P(A) = P(smokes) = 1/5 = .2
P(B | A) = P(age 25 - 44 | smokes) = 6 / 25 = .24
P(smokes and age 25 - 44) = .2 * .24 = .048 = 4.8% = 6/125