According to information provided by proponents of abstinence-only education, half of the gay male teenagers in the United States have tested positive for the AIDS virus. Proponents of abstinence-only education also teach that condoms fail to prevent HIV transmission during heterosexual intercourse as often as 31% of the time. Teens make up about 10% of the U.S. population at present, and the U.S. population is roughly 295 million.
Assume the following:
1) Presently 50% of gay male teens harbor the HIV virus.
1) HIV-positive gay teens do not self-sort according to HIV status; i.e., intercourse between gay teens is random with respect to HIV infection.
2) Condoms fail during homosexual intercourse as often as during heterosexual intercourse (proponents of abstinence-only sex education probably believe that condoms fail more often during homosexual intercourse, but I haven't been able to find statistics to this effect).
3) Gay teens have intercourse only with other gay teens, and not with any opposite-sex partners, or straight or bisexual male partners, or adults.
4) A gay teen meets a new sexual partner about every four months.
5) A gay teen has sex with a given sexual partner, on average, ten times before moving on to the next.
Question 1: Given these assumptions, what percentage of this group will be HIV-positive in a) four months? b) Eight months? c) A year? SHOW YOUR WORK!
Question 2: Given your results, do these statistics and assumptions seem to be plausible? Why or why not? If the statistics and assumptions are inaccurate, what seems like the most reasonable correction? Defend your answer.
See comments for answers.