Problem 1TE

There are N distinct types of coupons, and each time one is obtained it will, independently of past choices, be of type i with probability Pi, i = 1,.... N. Let T denote the number one need select to obtain at least one of each type. Compute P{T = n}.

Answer

Step 1 of 1

(a)

There are distinct types of coupons, and each time one is obtained it will, independently of past choices, be of type with probability

Let denote the number one need select to obtain at least one of each type.

We are asked to compute

Let

We know the following relationship of addition rule for selections.

Hence we can write that

……..(1)

……..(2)

Hence we can write and you can substitute the value of equation (1) and (2)