1
JEE Main 2016 (Offline)
+4
-1
Let two fair six-faced dice $$A$$ and $$B$$ be thrown simultaneously. If $${E_1}$$ is the event that die $$A$$ shows up four, $${E_2}$$ is the event that die $$B$$ shows up two and $${E_3}$$ is the event that the sum of numbers on both dice is odd, then which of the following statements is $$NOT$$ true?
A
$${E_1}$$ and $${E_2}$$ are independent.
B
$${E_2}$$ and $${E_3}$$ are independent.
C
$${E_1}$$ and $${E_3}$$ are independent.
D
$${E_1},$$ $${E_2}$$ and $${E_3}$$ are independent.
2
JEE Main 2015 (Offline)
+4
-1
If $$12$$ different balls are to be placed in $$3$$ identical boxes, then the probability that one of the boxes contains exactly $$3$$ balls is :
A
$$220{\left( {{1 \over 3}} \right)^{12}}$$
B
$$22{\left( {{1 \over 3}} \right)^{11}}$$
C
$${{55} \over 3}{\left( {{2 \over 3}} \right)^{11}}$$
D
$$55{\left( {{2 \over 3}} \right)^{10}}$$
3
JEE Main 2014 (Offline)
+4
-1
Let $$A$$ and $$B$$ be two events such that $$P\left( {\overline {A \cup B} } \right) = {1 \over 6},\,P\left( { {A \cap B} } \right) = {1 \over 4}$$ and $$P\left( {\overline A } \right) = {1 \over 4},$$ where $$\overline A$$ stands for the complement of the event $$A$$. Then the events $$A$$ and $$B$$ are :
A
independent but not equally likely.
B
independent and equally likely.
C
mutually exclusive and independent.
D
equally likely but not independent.
4
JEE Main 2013 (Offline)
+4
-1
Out of Syllabus
A multiple choice examination has $$5$$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $$4$$ or more correct answers just by guessing is :
A
$${{17} \over {{3^5}}}$$
B
$${{13} \over {{3^5}}}$$
C
$${{11} \over {{3^5}}}$$
D
$${{10} \over {{3^5}}}$$
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