Due to its confidence in quality control, the videocassette recorder manufacturer offers a full

replacement guarantee if a recorder fails within $2$ years. Based on compiled data, the

company observed that only $1\%$ of its recorders failed in the first year, while $5\%$ of recorders

that passed the first year failed in the second year. The warranty does not cover replacement

loggers$.$

a$.$ Formulate the evolution of a logger$\text{'}$s state as a Markov chain with two absorbed states

related to honoring the guarantee or the logger passing the guarantee period. Then $($one step$)$

construct the transition matrix.

b$.$ Find the possibility that the manufacturer will need to honor the warranty.