Probability Tes...

A man is known to speak the truths $$3$$ out of $$4$$ times. He throw a die and report that it is six. The probability that it is actually a six, is

Let $$u_1$$ and $$u_2$$ be two urns such that $$u_1$$ contains 3 white, 2 red balls and $$u_2$$ contains only 1 white ball. A fair coin is tossed. If head appears, then 1 ball is drawn at random from urn $$u_1$$ and put into $$u_2$$. However, if tail appears, then 2 balls are drawn at random from $$u_1$$ and put into $$u_2$$. Now, 1 ball is drawn at random from $$u_2$$. Then, probability of the drawn ball from $$u_2$$ being white is

If r.v$$X$$: waiting time in minutes for bus and p.d.f of $$X$$ is given by
$$f(x)=\begin{cases} \cfrac { 1 }{ 5 } ,0\le x\le 5 \\ 0,\quad otherwise \end{cases}$$
then probability of waiting time not more than $$4$$ minutes is $$=$$...........

The probability distribution of $$X$$ is

If two events $$A$$ and $$B$$ are such that $$P({ A }^{ C })=0.3,P(B)=0.4$$ and $$P({ AB }^{ C })=0.5$$, then $$P\left[ B/\left( A\cup { B }^{ C } \right)  \right] $$ is equal to

For the following distribution function $$F(x)$$ of a r.v $$X$$ is given

A biased coin with probability P, (0 < p < 1 ) of heads is tossed until a head appear for the first time. If the  probability that the number of tosses required is even is $$\frac{2}{5}$$ then P =  

From an urn containing six balls, $$3$$ white and $$3$$ black ones, a person selects at random an even number of balls (all the different ways of drawing an even number of balls are considered equally probable, irrespective of their number). 

The letters of the work "Questions" are arranged in a row at random.The probability that there are exactly two letters between Q and S is.