The Land of Oz

[BMAD]

The Land of Oz is blessed by many things, but not by good weather. They never have two nice days

in a row. If they have a nice day, they are just as likely to have snow as rain the next day. If they have snow or rain, they have an even chance of having the same the next day. If there is change from snow or rain, only half of the time is this a

change to a nice day.

How is the weather 15 days from now if there is a equal probability of each type of weather today (probability of each type)?

[bushindo]

what do you mean by an "even chance" of getting snow or rain?

never mind, i explained the wrong part. If it rained today then there is a 50% chance of rain again and 50% it won't

If I'm parsing the probability correctly

The problem is equivalent to the following. Let A be the matrix

         0    0.2500    0.2500
    0.5000    0.5000    0.2500
    0.5000    0.2500    0.5000

And let b be the vector [1/3 1/3 1/3]', where the elements from left to right correspond to chance of nice day, snow, and rain, respectively. What is the quantity A¹⁵ * b?

Turns out that A¹⁵ * b is approximately [1/5 2/5 2/5]. So chance of nice day is 1/5, chance of snow is 2/5, and chance of rain is 2/5.

[flamebirde]

what do you mean by an "even chance" of getting snow or rain?

[BMAD]

what do you mean by an "even chance" of getting snow or rain?

even chance of getting snow, rain, or pretty day

[BMAD]

what do you mean by an "even chance" of getting snow or rain?

never mind, i explained the wrong part. If it rained today then there is a 50% chance of rain again and 50% it won't

[bonanova]

Agree with Bushindo and note it converges rather quickly.

After only a few days it's a fraction of a percent from the limit values.