[CatoRenasci]

From my graduate work in econometrics and statistics some 30 years ago, I believe you are correct. Those coin toss examples always turned on the fact that each event was independent of the prior and subsequent events. I view the HIV/AIDS example as one of those problems where pure statistical probability is meaningless anyway: even if the probability of any event resulting in infection, and even if the events are independent of each other, the downside of infection (probable death) is so great that the expected value of the event happening would have to be very very highly negative.

[DB]

If heads is an infection and you toss the coin 10 times even though each time the chances of getting an infection is 50% the overall chances of being infected after the 10 tosses is 99.9%.