Market research shows that if a person buys Brand X, the probability that they will buy Brand X next time is 0.75. If a person buys Brand Y, the probability that they will buy B the next time is 0.55.

Keith bought Brand X today.

a) Write the initial probability matrix and the transition matrix

b) what is the probability that keith will switch to Brand Y on his next purchase

My first reaction was for initial matrix Po= [ 0.75, 0.55] ???

for transition it would be

0.75 0.25

0.45 0.55

Please help