# prob matrices

Hi,

I dont understand how to work this out.

Victoria Jones runs a small business making and selling statues of her cousin the adventurer Tasmania Jones.
The statues are made in a mould, then finished (smoothed and then hand-painted using a special gold paint) by
Victoria herself. Victoria sends the statues in order of completion to an inspector, who classifies them as either
‘Superior’ or ‘Regular’, depending on the quality of their finish.
If a statue is Superior then the probability that the next statue completed is Superior is p.
If a statue is Regular then the probability that the next statue completed is Superior is p – 0.2.

p on this day is 0.75.

On this day, a group of 3 consecutive statues is inspected. Victoria knows that the first statue of the 3 statues
is Regular.
ii. Find the expected number of these 3 statues that will be Superior.

how do work this out ? using matrices?
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Commented:
The first statue is Regular.

the probability that the second statue completed is Superior is p – 0.2
the probability that the second statue completed is Regular is 1-(p – 0.2)

If the second statue is Superior (p – 0.2) then the probability that the third is Superior is p.
If the second statue is Regular (1-(p – 0.2)) then the probability that the third statue completed is Superior is p – 0.2.

The expected number of Superior third statues is (p – 0.2)*p +  (1-(p – 0.2)) * (p – 0.2)
The expected number of Superior second statues is p – 0.2
The expected number of Superior first statues is 0
0

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