Short Answer TypeA and B toss a coin alternatively till one of them gets a head and wins the game. If A starts the game, find the probability of his winning at his third toss.
Long Answer TypeLet P(A), 
be the probabilities of A's getting the head and not getting the head respectively, then
Similarly, 
Let A start the game. He can win in the first throw, 3rd throw, 5th throw and so on.
Probability of A's winning in first throw = P(A) = 
Probability of A's winning in 3rd throw
Since all these cases are mutually exclusive
probability of A's winning the game first is
Since either A or B wins
probability of B's winning the game first = 
Short Answer TypeThere are three urns A, B and C. Urn A contains 4 white balls and 5 blue balls. Urn B contains 4 white balls and 3 blue balls. Urn C contains 2 white balls and 4 blue balls. One half is drawn from each of these urns. What is the probability that out of these three balls drawn, two are white balls and one is a blue ball?
An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?
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