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A laboratory animal may eat any one of three foods each day. Laboratory records show that if the animal chooses one food on one trial, it will choose the same food on the next trial with a probability of $50 \%,$ and it will choose the other foods on the next trial with equal probabilities of 25$\% .$a. What is the stochastic matrix for this situation?b. If the animal chooses food $\# 1$ on an initial trial, what is the probability that it will choose food $\# 2$ on the second trial after the initial trial?

a. $P = \left[ \begin{array} { c c c } { .5 } & { .25 } & { .25 } \\ { .25 } & { .5 } & { .25 } \\ { .25 } & { .25 } & { .5 } \end{array} \right]$b. the probability that the animal will choose food $\# 2$ is .3125

Calculus 3

Chapter 4

Vector Spaces

Section 9

Applications to Markov Chains

Vectors

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Okay, So have a P matrix of points wide 0.25 What you find to five here? Fine. Why put too fine. You point your fight. So let's say this Executive One two on three. Okay, Now we're asked. We were given our state victor, our initial vector, which is one no one we want to put out. We get quite five 0.25 important to flight. Okay, now let's multiply. P times are in a director, Our little dish x one and it's multiply P Temper X one back there. That gives us what? Why, What if I point you flying kind here and put fire rest of fortune five everywhere. Okay, It was an excellent actor. That was 0.5 point 25 0.25 And that just gives me play. 375 0.3125 0.3 once in flight through. So the probability of getting are true. The food three is 30.312

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