Problem 1

Probability Puzzle: - M-022703

To encourage Sanjeev's promising tennis career, his father offers him a prize if he wins (at least) two tennis sets in a row in a three-set series to be played with his father and the club champion alternately: father-champion-father or champion-father-champion, according to Sanjeev's choice. The champion is a better player than Sanjeev's father. Which series should Sanjeev choose?

Problem 2

AC is a diameter of a circle. Point B is on the circle such that AB=8 and BC=6. Point D is another point on the circle such that BD bisects angle ABC. Calculate BD as a simplified radical.

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