Probability Tes...

Suppose that two cards are drawn at random from a deck of cards. Let $$X$$ be the number of aces obtained. Then the value of $$E\left(X\right)$$ is

A bag A contains 4 green  and 6 red balls. Another bag B contains 3 green and 4 red balls. If one ball is drawn from each bag, find the probability that both are green.

A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year-III, 150 Year-II and 200 Year-I students who applied. Each Year-III's name is placed in the lottery 3 times; each Year-II's name, 2 times and Year-I's name, 1 time. What is the probability that a Year-III's name will be chosen?

In a class, 40% of the students study math and science. 60% of the students study math. What is the probability of a student studying science given he/she is already studying math?

If $$P\left( A|B \right) > P\left( A \right) $$, then which of the following is correct

A bag contains 5 red and 3 green balls. Another bag contains 4 red and 6 green balls. If one ball is drawn from each bag . Find the probability that one ball is red and one is green ?

A speaks truth in 75% of cases and B in 80% of cases. In what percent of cases are they likely to contradict each other in narrating the same event?

Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are $$\displaystyle \frac { 1 }{ 4 } ,\frac { 1 }{ 2 } $$ and $$\displaystyle \frac { 5 }{ 8 } $$, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?

A parents has two children. If one of them is boy, then the probability that other is, also a boy, is

If $$A$$ and $$B$$ are two events such that $$P\left( A \right) \neq 0$$ and $$P\left( B|A \right) =1$$, then