1
IIT-JEE 1999
MCQ (More than One Correct Answer)
+3
-0.75
The probabilities that a student passes in Mathematics, Physics and Chemistry are $$m, p$$ and $$c,$$ respectively. Of these subjects, the student has a $$75%$$ chance of passing in at least one, a $$50$$% chance of passing in at least two, and a $$40$$% chance of passing in exactly two. Which of the following relations are true?
A
$$p+m+c=19/20$$
B
$$p+m+c=27/20$$
C
$$pmc=1/10$$
D
$$pmc=1/4$$
2
IIT-JEE 1998
MCQ (More than One Correct Answer)
+2
-0.5
If $$\overline E$$ and $$\overline F$$ are the complementary events of events $$E$$ and $$F$$ respectively and if $$0 < P\left( F \right) < 1,$$ then
A
$$P\left( {E/F} \right) + P\left( {\overline E /F} \right) = 1$$
B
$$P\left( {E/F} \right) + P\left( {E/\overline F } \right) = 1$$
C
$$P\left( {\overline E /F} \right) + P\left( {E/\overline F } \right) = 1$$
D
$$P\left( {E/\overline F } \right) + P\left( {\overline E /\overline F } \right) = 1$$
3
IIT-JEE 1995 Screening
MCQ (More than One Correct Answer)
+2
-0.5
Let $$0 < P\left( A \right) < 1,0 < P\left( B \right) < 1$$ and
$$P\left( {A \cup B} \right) = P\left( A \right) + P\left( B \right) - P\left( A \right)P\left( B \right)$$ then
A
$$P\left( {B/A} \right) = P\left( B \right) - P\left( A \right)$$
B
$$P\left( {A' - B'} \right) = P\left( {A'} \right) - P\left( {B'} \right)$$
C
$$P\left( {A \cup B} \right)' = P\left( {A'} \right) - P\left( {B'} \right)$$
D
$$P\left( {A/B} \right) = P\left( A \right)$$
4
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
$$\,P\left( E \right) = 1/4,P\left( F \right) = 1/3$$
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