IIT-JEE 1999 | Probability Question 72 | Mathematics

IIT-JEE 1999

MCQ (More than One Correct Answer)

-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?

$$p+m+c=19/20$$

$$p+m+c=27/20$$

$$pmc=1/10$$

$$pmc=1/4$$

IIT-JEE 1998

MCQ (More than One Correct Answer)

-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

$$P\left( {E/F} \right) + P\left( {\overline E /F} \right) = 1$$

$$P\left( {E/F} \right) + P\left( {E/\overline F } \right) = 1$$

$$P\left( {\overline E /F} \right) + P\left( {E/\overline F } \right) = 1$$

$$P\left( {E/\overline F } \right) + P\left( {\overline E /\overline F } \right) = 1$$

IIT-JEE 1995 Screening

MCQ (More than One Correct Answer)

-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

$$P\left( {B/A} \right) = P\left( B \right) - P\left( A \right)$$

$$P\left( {A' - B'} \right) = P\left( {A'} \right) - P\left( {B'} \right)$$

$$P\left( {A \cup B} \right)' = P\left( {A'} \right) - P\left( {B'} \right)$$

$$P\left( {A/B} \right) = P\left( A \right)$$

IIT-JEE 1993

MCQ (More than One Correct Answer)

-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,

$$\,P\left( E \right) = 1/3,P\left( F \right) = 1/4$$

$$\,P\left( E \right) = 1/2,P\left( F \right) = 1/6$$

$$\,P\left( E \right) = 1/6,P\left( F \right) = 1/2$$

$$\,P\left( E \right) = 1/4,P\left( F \right) = 1/3$$

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