Probability Tes...

The different possibilities of distribution of $$2$$ black and $$2$$ white balls in two containers are as shown. Which of the following statements is true?

Let A and B be two events such that $$P(\overline{A\cup B})=\dfrac{1}{6}, P(A\cap B)=\dfrac{1}{4}$$ and $$P(\overline{A})=\dfrac{1}{4}$$, where $$\overline{A}$$ stands for the complement of the event A. Then the events A and B are?

If A and B are two mutually exclusive events, then?

A special die with number $$1$$, $$-1$$, $$2$$, $$-2$$, $$0$$ and $$3$$ is thrown thrice. The probability that total is $$6$$ is

The number of ways in which $$6$$ men can be arranged in a row, so that three particular men are consecutive, is 

If $$\displaystyle \frac{1+3p}{3}, \frac{1-p}{4}$$ and $$\dfrac{1-2p}{2}$$ are the probabilities of the three mutually exclusive events, then $$p \in $$

If $$\frac { 1+4p }{ 4 } ,\frac { 1-p }{ 4 } ,\frac { 1-2p }{ 4 } $$ are probabilities of three mutually exclusive and exclusive and exhaustive events, then the possible value of p belong to the set

In a class 5% of boys and 10% of girls have an I.Q of more than 150.In this class 60% of students are boys. If a student is selected at random and found to have an I.Q. of more than 150. Find the probability that the student is a boy.

Assume that the birth of a boy or girl to a couple to be equally likely ,mutually exclusive,independent of the other children in the family .for a couple having $$6$$ children ,the probability that their "three oldest are boys" is

There are $$n$$ distinct white and $$n$$ distinct black balls. The number of ways of arranging them in a row so that neighbouring balls are of different colours is: