Question

A ship is carrying 30 travelers from various great houses on a long sea voyage from Braavos to King’s Landing where they will participate in the Game of Thrones:

• 5 are from House Targaryen(TAR), and 5 from House Lannister (LAN)
• 4 are from House Stark (STA) and 4 from House Tyrell (TYR)
• 3 are from House Baratheon (BAR) and 3 from House Martell (MAR)
• 1 from each of the following houses: House Arryn (ARR), House Tully (TUL), House Greyjoy (GRE), House Bolton (BOL), House Frey (FRE), House Mormont(MOR)

You are now asked to evaluate probabilities relating to this voyage.

Unfortunately for the competitors, Braavos had an epidemic of the Heineken virus. Grand Maesters work around the clock to learn as much as they can about the Heineken virus.

• In their findings, they concluded that 1.1% of people coming from Braavos will test positive for the Heineken virus.
• They also know that there is a false negative rate of 4% and a false positive rate of 0.6%.

Use the information above to calculate the probability that a traveler who tests positive does actually have the Heineken virus. For this exercise, define the following events:

• T+: testing positive
• T-: testing negative
• V: having the Heineken virus
• H: being healthy

Answer 1