15 A sample of 200 households was obtained from a small town.
Each household was asked to complete a questionnaire about their purchases of takeaway food.
\(A\) is the event that a household regularly purchases Indian takeaway food.
\(B\) is the event that a household regularly purchases Chinese takeaway food.
It was observed that \(\mathrm { P } ( B \mid A ) = 0.25\) and \(\mathrm { P } ( A \mid B ) = 0.1\)
Of these households, 122 indicated that they did not regularly purchase Indian or Chinese takeaway food.
A household is selected at random from those in the sample.
Find the probability that the household regularly purchases both Indian and Chinese takeaway food.
[0pt] [6 marks]