Question

A medical researcher is studying the spread of a virus in a population of 1000 laboratory mice. During any week, there is a 90% probability that an infected mouse will overcome the virus, and during the same week there is a 30% probability that a noninfected mouse will become infected. One hundred mice are currently infected with the virus.

How many will be infected next week and in 2 weeks?

(a) next week

_______ mice

(b) in 2 weeks

_______ mice

Answer 1

a) 280

b) 244

Explanation:

a)

One hundred mice are currently infected with the virus and 900 are okay, so next week we should have 30% of 900 = 270 new infected mice and 90% of 100 = 90 recovered mice for a total of 370 - 90 = 280 infected mice.

b)

The following week we should have 30% of 1000 - 280 = 30% of 720 = 216 new infected mice and 90% of 280 = 252 recovered mice for a total of 280 + 216 - 252 = 244 infected mice.