Power outlets in HBL Suppose one evening during finals week

Power outlets in HBL Suppose one evening during finals week that you and X 1 people enter Babbidge Library in hopes of finding a place to study with an available electrical outlet. Often there are not enough to go around; tonight there are 20 outlets. Each visitor is equally likely to find (or miss out on) an outlet. Let A be the event that you find an outlet. (a) Find P[A | X = k]. [Hint: Consider the cases k 20 and k 21 separately.] (b) Suppose now you know also that X is given by a Poisson distribution with parameter 50. Find P[A]. (Express your answers in terms of a sum of two series, but don’t simplify further.)

Solution

Find P[A | X = k].

P( k < 20 ) 0 x-1

P( k > 21 ) 0 x

Suppose now you know also that X is given by a Poisson distribution with parameter 50. Find P[A]

P(A)= e^50 * 50^5 / 5! = 5.022786x10-16