1
AIEEE 2005
+4
-1
Let $$A$$ and $$B$$ 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 complement of event $$A$$. Then events $$A$$ and $$B$$ are :
A
equally likely and mutually exclusive
B
equally likely but not independent
C
independent but not equally likely
D
mutually exclusive and independent
2
AIEEE 2004
+4
-1
Out of Syllabus
The mean and the variance of a binomial distribution are $$4$$ and $$2$$ respectively. Then the probability of $$2$$ successes is :
A
$${28 \over 256}$$
B
$${219 \over 256}$$
C
$${128 \over 256}$$
D
$${37 \over 256}$$
3
AIEEE 2004
+4
-1
The probability that $$A$$ speaks truth is $${4 \over 5},$$ while the probability for $$B$$ is $${3 \over 4}.$$ The probability that they contradict each other when asked to speak on a fact is :
A
$${4 \over 5}$$
B
$${1 \over 5}$$
C
$${7 \over 20}$$
D
$${3 \over 20}$$
4
AIEEE 2003
+4
-1
Events $$A, B, C$$ are mutually exclusive events such that $$P\left( A \right) = {{3x + 1} \over 3},$$ $$P\left( B \right) = {{1 - x} \over 4}$$ and $$P\left( C \right) = {{1 - 2x} \over 2}$$ The set of possible values of $$x$$ are in the interval.
A
$$\left[ {0,1} \right]$$
B
$$\left[ {{1 \over 3},{1 \over 2}} \right]$$
C
$$\left[ {{1 \over 3},{2 \over 3}} \right]$$
D
$$\left[ {{1 \ 3},{13 \over 3}} \right]$$
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