A recent article in the Oklahoma Daily suggested that marijuana is a gateway drug for harder drug use. The following fact – which we will take as accurate – was used to support their argument: 9 out of 10 "hard drug" users have previously used marijuana. Additionally, the newspaper also reported that 4 out of every 10 persons in the general population have admitted using marijuana and that 2 out of 10 persons in the general population have admitted using "harder" drugs. You now find out that one of your children has used marijuana. What is the probability of your child subsequently using some "hard drug" based on the information presented above?

We know that 9 out of 10 "hard drug" users have previously used marijuana. Additionally, the newspaper also reported that 4 out of every 10 persons in the general population have admitted using marijuana and that 2 out of 10 persons in the general population have admitted using "harder" drugs. We calculate the probability of your child subsequently using some "hard drug", and we get:

[tex]P=\frac{9}{10}\cdot \frac{4}{10}\cdot \frac{2}{10}\\\\P=\frac{9}{125}\\\\P=0.072[/tex]

Therefore, the probability is P=0.072.