Question

An instructor with a cold enters the classroom and sneezes Poi(λ) (namely Poisson λ) times. From each sneeze, you catch the cold with probability p, independent of all other sneezes. Catching the cold from one sneeze suffices to get the cold. Find a simple expression (not an infinite sum) for the probability that at the end of the class you have the cold for:

(a)p= 1,

(b) general p. You may want to verify that p= 1 yields the answer in part (a).

Answer 1