Q:

Basic AND Probability from Given Data

In a particular week, the probability of a household purchasing cheese in any week was $20\%$ in England and $10\%$ in the rest of the UK. $75\%$ of the households sampled were in England. 
Calculate the probability that a randomly selected household from the sample is not England and did not buy cheese.

From data:
where $C$ is the event of buying cheese and $E$ the event of living in England,
$P(E)=0.75$   and $P(E')=0.25$
$P(C\mid E)=0.2$ and $P(C\mid E')=0.1$
Find $P(C'\cap E')$
as $P(C\mid E')=0.1,\, P(C'\mid E')=1-0.1=0.9$
$P(C'\cap E')=P(C'\mid E')P(E')$
$=0.9 \times 0.25=0.225$
The issue is my textbook says $P(C'\cap E')=0.025$ ????
Have I made a mistake or is the textbook wrong?

A:

Imagine polling 1000 people.  75%, so 750 people, are from England, 250 are not.  Of the 250 not from England, 10%, 25 purchase cheese, 225 do not.  Of the 1000 people, 225 are not from England and did not purchase cheese so the probability a person polled is not from England and did not purchase cheese is 225/1000= 0.225 or 22.5%.

