Probability If a person who takes a vaccine shot has 20 chan

Probability. If a person who takes a vaccine shot has 20% chance of catching a disease, and a person who lives in the same house of someone with the disease have 80% chance of catching the disease, what is the probability of someone who lives in the same house with a person with the disease and had take the vaccine catch the disease? Show steps and explanation.

Solution

as we know that the probability that take a vaccine shot and catiching a disease is 20% = 0.20

and we know that a person who lives in the same house of someone with the disease have 80% chance of catching the disease

so the probability of someone who lives in the same house with a person with the disease and had take the vaccine catch the disease is

0.20 * 0.80 = 0.16 = 16%