In 1000 people in a company, the probability of having a disease is 0.005. One of the people is John and he knows he has the disease. What does John think is the probability that more than 1 person including himself has the disease?

I would denote J to be the number of people with the disease excluding john.

The answer is J~Bin(999, p) P(J>0) = 0.993

Can someone explain to me what is happening? How do you have the p?