1
IIT-JEE 1993
MCQ (More than One Correct Answer)
+2
-0.5
$$E$$ and $$F$$ are two independent events. The probability that both $$E$$ and $$F$$ happen is $$1/12$$ and the probability that neither $$E$$ nor $$F$$ happens is $$1/2.$$ Then,
A
$$\,P\left( E \right) = 1/3,P\left( F \right) = 1/4$$
B
$$\,P\left( E \right) = 1/2,P\left( F \right) = 1/6$$
C
$$\,P\left( E \right) = 1/6,P\left( F \right) = 1/2$$
D
$$\,P\left( E \right) = 1/4,P\left( F \right) = 1/3$$
2
IIT-JEE 1991
MCQ (More than One Correct Answer)
+2
-0.5
For any two events $$A$$ and $$B$$ in a simple space
A
$$P\left( {A/B} \right) \ge {{P\left( A \right) + P\left( B \right) - 1} \over {P\left( B \right)}},P\left( B \right) \ne 0$$ is always true
B
$$P\left( {A \cap \overline B } \right) = P\left( A \right) - P\left( {A \cap B} \right)\,\,$$ does not hold
C
$$P\left( {A \cup B} \right) = 1 - P\left( {\overline A } \right)P\left( {\overline B } \right),$$ if $$A$$ and $$B$$ are independent
D
$$P\left( {A \cup B} \right) = 1 - P\left( {\overline A } \right)P\left( {\overline B } \right),$$ if $$A$$ and $$B$$ are disjoint.
3
IIT-JEE 1989
MCQ (More than One Correct Answer)
+2
-0.5
If $$E$$ and $$F$$ are independent events such that $$0 < P\left( E \right) < 1$$ and $$0 < P\left( F \right) < 1,$$ then
A
$$E$$ and $$F$$ are mutually exclusive
B
$$E$$ and $${F^c}$$ (the complement of the event $$F$$) are independent
C
$${E^c}$$ and $${F^c}$$ are independent
D
$$P\left( {E|F} \right) + P\left( {{E^c}|F} \right) = 1.$$
4
IIT-JEE 1988
MCQ (More than One Correct Answer)
+2
-0.5
For two given events $$A$$ and $$B,$$ $$P\left( {A \cap B} \right)$$
A
not less than $$P\left( A \right) + P\left( B \right) - 1$$
B
not greater than $$P\left( A \right) + P\left( B \right)$$
C
equal to $$P\left( A \right) + P\left( B \right) - P\left( {A \cup B} \right)\,\,$$
D
$$P\left( A \right) + P\left( B \right) + P\left( {A \cup B} \right)\,\,$$
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