Researchers at the Institute for Zombie Awareness and Prevention have discovered that 40% of people with red hair are immune to the zombie virus and 5% of non redheads are immune. The percentage of redheads world wide is 2%.

(a) What is the probability that a person bitten at random will not become a zombie?

(b) What is the probability that a person is redheaded if we already know they are immune to zombism?

(c) The largest concentration of redheads in the world is Scotland, where 13% of the population is redheaded. What is the probability a person randomly selected in Scotland is immune?