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:

$\frac{1}{3}$

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 = $\frac{1}{3}×\frac{60}{100}+\frac{1}{3}×\frac{70}{100}+\frac{1}{3}×\frac{80}{100}=\frac{7}{10}$

$P(B|T)=\frac{P(B)×P(T|B)}{Total\, probability\, of\, trust}$

$=\frac{\frac{1}{3}×\frac{70}{100}}{\frac{7}{10}}=\frac{1}{3}$