1
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.
2
JEE Main 2013 (Offline)
+4
-1
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
$${{10} \over {{3^5}}}$$
3
AIEEE 2012
+4
-1
Three numbers are chosen at random without replacement from $$\left\{ {1,2,3,..8} \right\}.$$ The probability that their minimum is $$3,$$ given that their maximum is $$6,$$ is :
A
$${3 \over 8}$$
B
$${1 \over 5}$$
C
$${1 \over 4}$$
D
$${2 \over 5}$$
4
AIEEE 2011
+4
-1
Consider $$5$$ independent Bernoulli's trials each with probability of success $$p.$$ If the probability of at least one failure is greater than or equal to $${{31} \over 32},$$ then $$p$$ lies in the interval
A
$$\left( {{3 \over 4},{{11} \over {12}}} \right]$$
B
$$\left[ {0,{1 \over 2}} \right]$$
C
$$\left( {{11 \over 12},1} \right]$$
D
$$\left( {{1 \over 2},{{3} \over {4}}} \right]$$
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