Probability
Bayes' theorem; conditional probability
Grade Class 12
Question:
Class XII has sections A (40%) and B (60%). 20% students get into IIT. $P$(IIT from A)$=5P$(IIT from B). A student not selected in IIT is chosen. Probability he is from section B is
$\dfrac{4}{13}$
$\dfrac{5}{13}$
$\dfrac{9}{13}$
$\dfrac{10}{13}$
Step-by-Step Solution
Key Concept: Let $P$(IIT|B)$=p$. Then $P$(IIT|A)$=5p$. Given $0.4\cdot5p+0.6\cdot p=0.2$ (total selection rate). Solve for $p$, then use Bayes.
$P(B|\text{not IIT})=9/13$.
Correct Answer: 3