# Math2565M Solutions 4.12

### From MathWiki

Q)

A Shipping company can send a package through one of three cities (A, B, or C) before it gets to it's final destination. Two packages are sent by the company. An elementary event will determine which city each package goes through. Assume the package is equally likely to go through any of the cities. List the sample space for the possible cities through which the two packages might go.

a) Using classical probability assessment, determine the probability the first package did go and the second package did not go through city A.

b) Using classical probability assessment, determine the probability that neither of the packages went through city A.

A)

Sample space:

AA, AB, AC, BA, BB, BC, CA, CB, CC

a) P(A|not A) = 2/9 = 0.22

b) P(not A|not A) = 4/9 = 0.44