Your company is about to introduce a new detergent and you're interested in whether it will clean up in the market. It will be competing against three other existing brands. As a result of a small test market and interviews with consumers familiar with all four detergents, we have derived the following purchase transition matrix:

 

A

B

C

D

A

.75

.1

.05

.1

B

.4

.2

.1

.3

C

.1

.2

.4

.3

D

.2

.2

.3

.3

Our new detergent is brand A in this matrix. The interpretation of the matrix is, for example, if someone most recently purchased brand A, then with probability .75 his next purchase of this product will also be brand A. Similarly, someone who most recently purchased brand B will next purchase brand D with probability .3. An associate of yours who looked at this matrix said, "Aha, we should expect to get 75% of the market in the long run with brand A." Do you think your associate is correct?