httpimgurcomSARuJspSolutiona As X3 there are 3 customers Als

http://imgur.com/SARuJsp

Solution

a. As X=3, there are 3 customers. Also, Y=3, that is, there are 3 total packages. As packages per customer can only be 1,2, or 3, each of the 3 customers should have 1 package each.

P(X=3,Y=3) = P(X=3) * [P(package= 1 for a customer)]³ = 0.25 * 0.5³ = 0.0312

b. As X=4, there are 4 customers. Y=11 meaning that there are 11 packages. So 3 customers should have 3 packages each and 1 customer should have 2 packages. This can happen in:

4C1*3C3 = 4 number of ways.

P(X=4,Y=11) = 4*P(X=4)*[P(package= 3 for a customer)]³ [P(package= 2 for a customer)] = 4*0.15*0.25³ *0.25

= 0.0023