1
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2 Let E, F and G be three events having probabilities $$P(E) = {1 \over 8}$$, $$P(F) = {1 \over 6}$$ and $$P(G) = {1 \over 4}$$, and let P (E $$\cap$$ F $$\cap$$ G) = $${1 \over {10}}$$. For any event H, if Hc denotes the complement, then which of the following statements is (are) TRUE?
A
$$P(E \cap F \cap {G^c}) \le {1 \over {40}}$$
B
$$P({E^c} \cap F \cap G) \le {1 \over {15}}$$
C
$$P(E \cup F \cup G) \le {{13} \over {24}}$$
D
$$P({E^c} \cup {F^c} \cup {G^c}) \le {5 \over {12}}$$
2
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1 There are three bags B1, B2 and B3. The bag B1 contains 5 red and 5 green balls, B2 contains 3 red and 5 green balls, and B3 contains 5 red and 3 green balls. Bags B1, B2 and B3 have probabilities $${3 \over {10}}$$, $${3 \over {10}}$$ and $${4 \over {10}}$$ respectively of being chosen. A bag is selected at random and a ball is chosen at random from the bag. Then which of the following options is/are correct?
A
Probability that the chosen ball is green, given that the selected bag is B3, equals $${3 \over 8}$$.
B
Probability that the selected bag is B3, given that the chosen ball is green, equals $${5 \over 13}$$.
C
Probability that the chosen ball is green equals $${39 \over 80}$$.
D
Probability that the selected bag is B3 and the chosen ball is green equals $${3 \over 10}$$.
3
JEE Advanced 2017 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let X and Y be two events such that $$P(X) = {1 \over 3}$$, $$P(X|Y) = {1 \over 2}$$ and $$P(Y|X) = {2 \over 5}$$. Then
A
$$P(Y) = {4 \over {15}}$$
B
$$P(X'|Y) = {1 \over 2}$$
C
$$P(X \cup Y) = {2 \over 5}$$
D
$$P(X \cap Y) = {1 \over 5}$$
4
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
$${n_1} = 6,{n_2} = 12,{n_3} = 5,{n_4} = 20$$
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