TCS Company

-After the typist writes 12 letters and addresses 12 envelopes, she
inserts the letters randomly into the envelopes (1 letter per envelope).
What is the probability that exactly 1 letter is inserted in an improper
envelope?

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TCS Other Question

For the FIFA world cup, Paul the octopus has been predicting the
winner of each match with amazing success. It is rumored that in a match
between 2 teams A and B, Paul picks A with the same probability as A's
chances of winning. Let's assume such rumors to be true and that in a
match between Ghana and Bolivia, Ghana the stronger team has a
probability of 2/3 of winning the game. What is the probability that
Paul will correctly pick the winner of the Ghana-Bolivia game?
There are two boxes, one containing 10 red balls and the other
containing 10 green balls. You are allowed to move the balls between the
boxes so that when you choose a box at random and a ball at random from
the chosen box, the probability of getting a red ball is maximized. This
maximum probability is