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.

If $$P(E_k)\propto k$$ for $$0\leq k\leq n$$, then the probability that X is the only student to pass the examination is

If $$P(E_k)=C$$ for $$0\leq k\leq n$$, then $$P(A)$$ equals

If $$P(E_k)\propto k$$ for $$0\leq k\leq n$$, then $$\displaystyle \lim_{n\rightarrow \infty}\sum_{k=0}^nP(E_k|A)$$ equals

A box contain $$N$$ coins, $$m$$ of which are fair are rest and biased. The probability of getting a head when a fair coin is tossed is $$1/2$$, while it is $$2/3$$ when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. The first time it shows head and the second time it shows tail. The probability that the coin drawn is fair is

If $$P(E_k)\propto k$$ for $$0\leq k\leq n$$, the P(A) 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 $$\displaystyle \frac{31}{42}$$, then $$n$$ is equal to 

Given that she is successful, the chance she studied for 4 hours, 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. Find the probability the chosen urn was I.