The Creamiest Cone, a local ice cream shop, classifies sales each day as \"low,\

Question

The Creamiest Cone, a local ice cream shop, classifies sales each day as "low," "average," or "high." If sales are low one day, then there is a 20% chance they will be low the next day, a 40% chance they will be average the next day, and a 40% chance they will be high the next day. If sales are average one day, then they are always low the next day. If sales are high one day, then they are always low the next day.

In the long run, how often are the sales high? Write your answer as a fraction in lowest terms.?

Explanation / Answer

here for abiove transition matrix:

T=

let long run matrix is A =[x y 1-x-y]

hence AT=A

0.2x+y+1-x-y =x

1.8x=1

x =1/1.8=5/9

also 0.4x+0*y+(1-x-y)*0=y

y=0.4*5/9=2/9

hence in long run proportion of times sales is high=1-x-y =1-5/9-2/9=2/9

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