A) \[P(A/B)>P(A)\Rightarrow P(B/A)>P(B)\]
B) \[P\left( \frac{B}{A} \right)+(\bar{B}/\bar{A})=1\]
C) \[P(B/A)\ne P(B/A')\]only when A, B are independent
D) \[P(A/B)=P(A'/B)\] only when A, Bare mutually exclusive
Correct Answer: A
Solution :
Idea \[\therefore \]\[P(A/B)=\]probability of occurrence of A L given that B has already occur\[P(A/B)=\frac{P(A\cap B)}{P(B)}\]We know that \[P\left( \frac{A}{B} \right)>P(A)\] \[\frac{P(A\cap B}{P(B)}>P(A)\Rightarrow P(\cap B)>P(A)\cdot P(B)\] \[P\left( \frac{B}{A} \right)=\frac{P(A\cap B}{P(A)}>\frac{P(A)\cdot P(B)}{P(A)}\] \[P(B/A)>P(B)\] TEST Edge Different types of questions based on conditional probability are asked in JEE Main. Students are learn the formulae and definition of conditional probability and intersection or union of sets to solve such types of questions.
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