Virus Z is a new virus infecting people. Some people get Virus Zand develop no systems. In others, Virus X causes a disease calledDisease Z.
If you have Virus Z, you have it for life and everyone you touchgets Virus Z, if they didn’t have it already. (They get itimmediately when you touch them.) If you get Virus Z, you willeither immediately develop Disease Z, or you will never developDisease Z, and those two outcomes are equally likely. Differentpeople’s reactions to the virus are independent.
There is a 50% chance John has Virus Z. John does not haveDisease Z. John touches four people without Virus Z. Given that thefirst three do not develop Disease Z, what is the probability thatthe fourth one develops Disease Z?
