An insurance company determines that n, the number of claims received in a week, is a random variable with p[n = n] = 1/2n+1, where n > 0 . the company also determines that the number of claims received in a given week is independent of the number of claims received in any other week. determine the probability that exactly seven claims will be received during a given two week period.
(a) 1/256
(b) 1/128
(c) 7/512
(d) 1/64
(e) 1/32

(D)  

Step-by-step explanation:

Given : An insurance company determines that N, the number of claims received in a week, is a random variable with

, where n > 0 .

To determine the probability that exactly seven claims will be received during a given two week period.

Let n is the number of claims during first week ( ) the 7-n is the number of claims during second week  ( ).

Then , we have

[ ∵ The number of claims received in a given week is independent of the number of claims received in any other week. ]

=

Hence, the probability that exactly seven claims will be received during a given two week period =