In a musical chair game, the person playing the music has been advised to stop playing the music at any time within 2 minutes after she starts playing. What is the probability that the music will stop within the first half-minute after starting?

Consider a game played by 10 people in which each flips a fair up coin at the same time. If all but one of the coins comes up the same, then the odd persons wins (e.g., if there are nine tails and one head then head wins). If such a situation does not occur, the players flips again. Find the probability that game is settled on or after nth toss.

A train, initially at station A , starts its journey and eventually stops at station B after travelling a distance s . The first part of its journey is under uniform acceleration u and the later part under uniform retardation v . Show that the time taken for the journey is sqrt(2s((1)/(u)+(1)/(v))).