discrete prob. distribution

The number of times that Max gets cold in a year follows a Poisson distribution with a mean of 4. A health food manufacturer claims that if a person takes the health food produced by it, there is 80% of chance to reduce the average number of times he/ she gets a cold to 1 in a year and 20% to have no appreciable(可察覺的) effects. If Max has taken the health food for six months and he got a cold once during that period, find the probability that the health food is beneficial to him.