AIEEE 2005 | Probability Question 226 | Mathematics

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 :

equally likely and mutually exclusive

equally likely but not independent

independent but not equally likely

mutually exclusive and independent

AIEEE 2005

MCQ (Single Correct Answer)

-1

A random variable $$X$$ has Poisson distribution with mean $$2$$.
Then $$P\left( {X > 1.5} \right)$$ equals :

$${2 \over {{e^2}}}$$

$$0$$

$$1 - {3 \over {{e^2}}}$$

$${3 \over {{e^2}}}$$

AIEEE 2004

MCQ (Single Correct Answer)

-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 :

$${4 \over 5}$$

$${1 \over 5}$$

$${7 \over 20}$$

$${3 \over 20}$$

AIEEE 2004

MCQ (Single Correct Answer)

-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 :

$${28 \over 256}$$

$${219 \over 256}$$

$${128 \over 256}$$