Probability Tes...

Let $$\mathrm{E}^{\mathrm{c}}$$ denote the complement of an event $$\mathrm{E}$$. Let $$\mathrm{E},\ \mathrm{F},\ \mathrm{G}$$ be pairwise independent events with $$\mathrm{P}(\mathrm{G})>0$$ and $$\mathrm{P}(\mathrm{E}\,\mathrm{\cap}\,\mathrm{F}\,\mathrm{\cap}\,\mathrm{G}) =0$$. Then $$\mathrm{P}(\mathrm{E}^{\mathrm{c}}\,\mathrm{\cap}\,\mathrm{F}^{\mathrm{c}}|\mathrm{G})$$ equals 

A signal which can be green or red with probability $$\displaystyle \frac{4}{5}$$ and $$\displaystyle \frac{1}{5}$$ respectively, is received by station $$\mathrm{A}$$ and then transmitted to station $$\mathrm{B}$$. The probability of each station receiving the signal correctly is $$\displaystyle \frac{3}{4}$$. If the signal received at station $$\mathrm{B}$$ is green,  then the probability that the original signal was green is

For $$i=1, 2, 3, 4$$ let $$T_i$$ denote the event that the students $$S_i$$ and $$S_{i+1}$$ do NOT sit adjacent to each other on the day of the examination. Then the probability of the event $$T_1 \cap T_2 \cap T_3 \cap T_4$$ is?

The probability that, on the examination day, the student $$S_1$$ gets the previously allotted seat $$R_1$$ and None of the remaining students gets the seat previously allotted to him/her is?

A bag contains 12 balls out of which x are white.If one ball is drawn at random, what is the probability it will be a white ball?

A pack of playing cards was found to contain only $$51$$ cards. If the first $$13$$ cards which are examined are all red, then the probability thatthe missing card is black, is

If $$P(A) + P(B) = 1$$; then which of the following option explains the event $$A$$ and $$B$$ correctly ?

A bag contains 40 balls out of which some are red, some are blue and remaining are black. If the probability of drawing a red ball is $$\displaystyle \frac{11}{20}$$ and that of blue ball is $$\displaystyle \frac{1}{5}$$, then the number of black ball is?

There are 50 marbles of 3 colors: blue yellow and black The probability of picking up a blue marble is 3/10 and that of picking up a yellow marble is 1/2 The probability of picking up a black ball is 

A bag contains six red four green and eight white balls If a ball is picked at random the probability that it is not white is