Probability Tes...

An employer sends a letter to his employee but he does not receive the reply (It is certain that employee would have replied if he did receive the letter). It is known that one out of $$n$$ letters does not reach its destination. Find the probability that employee does not receive the letter.

A sample of size $$4$$ is drawn with replacement (without replacement )from an urn containing $$12$$ balls, of which $$8$$ are white, what is the conditional probability that the ball drawn on the third draw was white, given that the sample contains $$3$$ white balls ?

Let $$E, F, G$$ be pairwise independent events with $$P(G) > 0$$ and $$P(E\cap F\cap G)=0$$. Then $$P(E'\cap F'|G)$$ equals

A bag contains $$ (2n+1)$$ coins. It is known that  $$n$$ of these coins have a head on both sides, whereas the remaining  $$(n+1)$$  coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is $$\dfrac{31}{42}$$, then  $$n$$ is equal to

There are two balls in an urn whose colours are not known (each ball can be either white or black). A white ball is put into the urn. A ball is drawn from the urn. The probability that it is white is

A bag contains some white and some black balls, all combinations of balls 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

A bag contains some white and some black balls, all combinations of balls 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

A letter is known to have come from either $$TATANAGAR$$ or $$CALCUTTA$$. On the envelope just two consecutive letters $$TA$$ are visible. The probability that the letter has come from $$CALCUTTA$$ is

A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is

The conditional probability that $$X\geq 6$$ given the $$X > 3$$ equals