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:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{1}{3}$
$P(T|A)=\frac{60}{100},P(T|B)=\frac{70}{100},P(T|C)=\frac{80}{100}$
T → trust of former in new technology probability to choose any mohalla = $\frac{1}{3}$
so total probability = $\frac{1}{3}×\frac{60}{100}+\frac{1}{3}×\frac{70}{100}+\frac{1}{3}×\frac{80}{100}=\frac{7}{10}$
$P(B|T)=\frac{P(B)×P(T|B)}{Total\, probability\, of\, trust}$
$=\frac{\frac{1}{3}×\frac{70}{100}}{\frac{7}{10}}=\frac{1}{3}$