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%.
The total probability that a farmer believes in new technology of agriculture is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{7}{10}$
$P(T|A)=\frac{60}{100},P(T|B)=\frac{70}{100},P(T|C)=\frac{80}{100}$
T → trust of former in new technology probability to choose any mohalla = $\frac{1}{3}$
so total probability = $\frac{1}{3}×\frac{60}{100}+\frac{1}{3}×\frac{70}{100}+\frac{1}{3}×\frac{80}{100}$
$=\frac{7}{10}$