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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

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TCS Other Question

-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?
- A and B play a game of dice between them. The dice consist of colors
on their faces (instead of numbers). When the dice are thrown, A wins if
both show the same color; otherwise B wins. One die has 4 red face and 2
blue faces. How many red and blue faces should the other die have if the
both players have the same chances of winning?