Science:Math Exam Resources/Courses/MATH152/April 2022/Question B2 (a)/Statement

A grocery store sells three types of apples: Ambrosia, Braeburn, and Cameo. Every week, 20% of the people who bought Ambrosia last week switch to Braeburn, 10% switch to Cameo, and 70% buy Ambrosia again. Similarly, 20% of customers who bought Braeburn last week switch to Ambrosia, 20% switch to Cameo, and the remaining 60% buy Braeburn again. Those who bought Cameo last week, 20% switch to Ambrosia, 40% switch to Braeburn, and 40% stay with Cameo.

(a) Find the transition matrix of the corresponding random walk.