For two events A and B
Match List I with List II
| LIST I | LIST II | ||
| A. | $P(\overline{A}∩\overline{B})=P(\overline{A}).P(\overline{B})$ | I. | P(A/B)≥ P(A) |
| B. | A⊂ B and P(B) ≠ 0 | II. | P(A)=P(B) |
| C. | P(A ∪ B) =P(A) +P(B) | III. | A and B are independent events |
| D. | P(A|B)=P(B|A) | IV. | A and B are mutually exclusive events |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A-III, B-I, C-IV, D-II
A. $P(\overline{A}∩\overline{B})=P(\overline{A}).P(\overline{B})$ ⇒ A and B are independent events (III)
B. $A⊂B,P(B)≠0⇒P(A/B)=\frac{P(A)}{P(B)}$
as $P(B)≤1⇒\frac{P(A)}{P(B)}≥P(A)$ → (I)
C. $P(A ∪ B) =P(A) +P(B)$
$⇒P(A ∩ B)=0$ ⇒ A and B are mutually exclusive events (IV)
D. $P(A|B)=P(B|A)⇒\frac{P(A ∩ B)}{P(B)}=\frac{P(A ∩ B)}{P(A)}$
$⇒P(A)=P(B)$ (II)