Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: [Probability, University Introductory Level] "Rat Run" Question

Then we can form the transition matrix where the rows tells the probabilities of moving to any room (columns).

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

jakndaxta

Member

Registered: 2016-03-15

Posts: 18

Re: [Probability, University Introductory Level] "Rat Run" Question

Then we can form the transition matrix where the rows tells the probabilities of moving to any room (columns).

Makes sense to me so far!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: [Probability, University Introductory Level] "Rat Run" Question

The initial state vector is [0,0,0,1] which means the mouse starts in room 4. We could have specified [1/2, 0, 1/2, 0] which would mean that the mouse could start in either room 1 or room 3 and the probability of either is 1/2. But for our example it is [0,0,0,1]. This mouse is kind of lazy each day he wanders into another legal room and stays for one day. He does this at random based on the probabilities given in the matrix.

We would like to know what is the probability that on the 3rd day he is in room 2.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.