Math
posted by Kimberly .
To determine what effect the salespeople had on purchases, a department store polled 700 shoppers as to whether or not they had made a purchase and whether or not they were pleased with the service. Of those who had made a purchase, 125 were happy with the service and 111 were not. Of those who had made no purchase, 148 were happy with the service and 316 were not.
Find the probability that a shopper who was happy with the service had made a purchase (round the answer to the nearest hundredth).
What can you conclude?
About what percent of those who were happy with the service made a purchase?

the transition matrix would be
..... : happy not happy
....buy 125/236 111/236
not buy 148/464 316/464 or
│.53 .47 │
│.32 .68 │
so [a b] x [transition matrix] = [a b]
where a+b= 1
I got .53a + .32b = a or 32b = 47a
and .47a + .68b = b
we only need the first of these relations and the fact that a+b = 1
then a = 1b
and 32b = 47a
32b = 47(1b)
32b = 47  47b
79b = 47
b = .595 then a = .405
(This is the first time I have seen this kind of question in this forum, and its been over 12 years since I have done one like it. So I am not 100% sure of my work here)