1
JEE Advanced 2015 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $${n_1}$$ and $${n_2}$$ be the number of red and black balls, respectively, in box $${\rm I}$$. Let $${n_3}$$ and $${n_4}$$ be the number of red and black balls, respectively, in box $${\rm I}{\rm I}.$$

One of the two boxes, box $${\rm I}$$ and box $${\rm I}{\rm I},$$ was selected at random and a ball was drawn randomly out of this box. The ball was found to be red. If the probability that this red ball was drawn from box $${\rm I}{\rm I}$$ is $${1 \over 3},$$ then the correct option(s) with the possible values of $${n_1}$$ $${n_2},$$ $${n_3}$$ and $${n_4}$$ is (are)

A
$${n_1} = 3,{n_2} = 3,{n_3} = 5,{n_4} = 15$$
B
$${n_1} = 3,{n_2} = 6,{n_3} = 10,{n_4} = 50$$
C
$${n_1} = 8,{n_2} = 6,{n_3} = 5,{n_4} = 20$$
D
$${n_1} = 6,{n_2} = 12,{n_3} = 5,{n_4} = 20$$
2
JEE Advanced 2015 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $${n_1}$$ and $${n_2}$$ be the number of red and black balls, respectively, in box $${\rm I}$$. Let $${n_3}$$ and $${n_4}$$ be the number of red and black balls, respectively, in box $${\rm I}{\rm I}.$$

A ball is drawn at random from box $${\rm I}$$ and transferred to box $${\rm I}$$$${\rm I}.$$ If the probability of drawing a red ball from box $${\rm I},$$ after this transfer, is $${1 \over 3},$$ then the correct option(s) with the possible values of $${n_1}$$ and $${n_2}$$ is(are)

A
$${n_1} = 4$$ and $${n_2} = 6$$
B
$${n_1} = 2$$ and $${n_2} = 3$$
C
$${n_1} = 10$$ and $${n_2} = 20$$
D
$${n_1} = 3$$ and $${n_2} = 6$$
3
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
$$P\left( {{X^c} \cap Y} \right) = {1 \over 3}$$
4
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
$$P\left[ {X|{X_1}} \right] = {7 \over {16}}$$
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