Standard +0.8 This is a multi-step conditional probability problem requiring students to set up and solve simultaneous equations using P(B|A), P(A|B), and the complement information. It demands careful algebraic manipulation of probability definitions (P(B|A) = P(A∩B)/P(A)) and systematic reasoning, going beyond routine conditional probability exercises but not requiring advanced techniques.
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 \(P(B|A) = 0.25\) and \(P(A|B) = 0.1\)
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. [6 marks]
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 $P(B|A) = 0.25$ and $P(A|B) = 0.1$
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. [6 marks]
\hfill \mbox{\textit{AQA Paper 3 Q15 [6]}}