Probability Tes...

A bag contains 6 balls. Two balls are drawn and found to be red. The probability that five balls in the bag are red

There are 3 boxes each having two drawers The first box contains a gold coin in each drawer. The second, a gold coin in one drawer and a silver coin in the other. The third box contains a silver coin in each drawer. A box is chosen at random and a drawer is opened. If a gold coin is found in that drawer, then the probability that the other drawer also contains a gold coin is 

The contents of urn I and II are as follows,
Urn I: 4 white and 5 black balls
Urn II : 3 white and 6 black balls
One urn is chosen at random and a ball is drawn and its colour is noted and replaced back to the urn. Again a ball is drawn from the same urn,
colour is noted and replaced. The process is repeated 4 times and as a result one ball of white colour and 3 of black colour are noted. The probability that the chosen urn was I is

If $$P(A)=0.3$$  and  $$P(A\cup B)=0.8, P(A-B)=0.1$$
then value of $$P(A/\overline{B})=$$

A bag contains 4 white and 5 black balls. A second bag contains 3 (identical) white and 6 (identical) black balls. One bag is chosen at random and a ball is drawn. Its colour is noted and the ball replaced. This is repeated four times. It was found that of these four, one was white and 3 were black. The $$n$$ the probability that the first bag was chosen is

Die $$A$$ has $$4$$ red and $$2$$ white faces where as die $$B$$ has two red and $$4$$ white faces. $$A$$ fair coin is tossed. If head turns up, the game continues by throwing die $$A$$, if tail turns up then die $$B$$ is to be used. If the first two throws resulted in red, what is the probability of getting red face at the third throw ?

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

A bag contains some white and some black balls, all combinations of ball being equally likely. The total number of balls in the bag is 10. If three balls are drawn at random without replacement and all of them are found to be black, the probability that the bag contains 1 white and 9 black balls is

In a class of $$10$$ students, probability of exactly $$i$$ students passing examination is directly proportional to $$i^2$$. If a student selected at random is found to have passed the examination, then the probability that he was the only student who has passed the examination is

Let A and B be two events such that $$ P(A \cap B^{c})=0.20, P( A^{c} \cap B)=0.15, P(A^{c} \cap B^{c})=0.1$$, then $$P(A/B)$$ is equal to