CUET · MATHS · PYQ PAPER 2023
In a village, there are three mohallas A, B and C. 60\% farmers in mohalla A believe in new technology of agriculture, while in B it is 70\% and in C is 80\%.
District agricultural officer selects a farmer at random and he found that the farmer believed in new technology of agriculture, then the probability that he belongs to mohalla B is:
- A \(\frac{2}{3}\)
- B \(\frac{3}{5}\)
- C \(\frac{3}{7}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{3}\)
Step-by-step Solution
Detailed explanation
\(P(T) = P(T|A)P(A) + P(T|B)P(B) + P(T|C)P(C)\) \(P(T) = (0.6 \times \frac{1}{3}) + (0.7 \times \frac{1}{3}) + (0.8 \times \frac{1}{3}) = \frac{1}{3}(0.6 + 0.7 + 0.8) = \frac{1}{3}(2.1) = 0.7\) \(P(B|T) = \frac{P(T|B)P(B)}{P(T)}\)…
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