1
IIT-JEE 2012 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$X$$ and $$Y$$ be two events such that $$P\left( {X|Y} \right) = {1 \over 2},$$ $$P\left( {Y|X} \right) = {1 \over 3}$$ and $$P\left( {X \cap Y} \right) = {1 \over 6}.$$ Which of the following is (are) correct ?
A
$$P\left( {X \cup Y} \right) = {2 \over 3}$$
B
$$X$$ and $$Y$$ are independent
C
$$X$$ and $$Y$$ are not independent
D
$$P\left( {{X^c} \cap Y} \right) = {1 \over 3}$$
2
IIT-JEE 2012 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
A ship is fitted with three engines $${E_1},{E_2}$$ and $${E_3}$$. The engines function independently of each other with respective probabilities $${1 \over 2},{1 \over 4}$$ and $${1 \over 4}$$. For the ship to be operational at least two of its engines must function. Let $$X$$ denote the event that the ship is operational and Let $${X_1},{X_2}$$ and $${X_3}$$ denote respectively the events that the engines $${E_1},{E_2}$$ and $${E_3}$$ are functioning. Which of the following is (are) true?
A
$$P\left[ {X_1^c|X} \right] = {3 \over {16}}$$
B
$$P$$ [exactly two engines of the ship are functioning $$\left. {|X} \right] = {7 \over 8}$$
C
$$P\left[ {X|{X_2}} \right] = {5 \over {16}}$$
D
$$P\left[ {X|{X_1}} \right] = {7 \over {16}}$$
3
IIT-JEE 2011 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$E$$ and $$F$$ be two independent events. The probability that exactly one of them occurs is $$\,{{11} \over {25}}$$ and the probability of none of them occurring is $$\,{{2} \over {25}}$$. If $$P(T)$$ denotes the probability of occurrence of the event $$T,$$ then
A
$$P\left( E \right) = {4 \over 5},P\left( F \right) = {3 \over 5}$$
B
$$P\left( E \right) = {1 \over 5},P\left( F \right) = {2 \over 5}$$
C
$$P\left( E \right) = {2 \over 5},P\left( F \right) = {1 \over 5}$$
D
$$P\left( E \right) = {3 \over 5},P\left( F \right) = {4 \over 5}$$
4
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
$$pmc=1/4$$
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