28. Case study: Probability

Two friends, Neha and Sneha, decided to play the game pockets billiard on their holiday. This game is similar to the carom game, except but it has \(6\) holes on the board to strike the balls into it. This game consists of \(15\) numbered color balls, and \(1\) cue ball, which is used to strike the other \(15\) numbered color balls to the holes. These balls are arranged in the pyramid form. The first player strikes them using the white ball(cue ball) to break the formation and then tries to sink the ball into the holes. Each player takes alternate turns to strike the balls.

 

(Note: Ignore the cue ball while taking the total number of balls.)

 

 

1. If Neha plays first, then the probability that she successfully sinks the ball numbered 10 is

 

2. If Sneha plays secondly without replacing the ball 10, then the probability that Sneha sink the ball numbered 13 is

 

3. The probability that Neha sinks a ball is an odd number is

 

4. The probability that Sneha sinks a ball is a number divisible by \(6\) is

 

5. The probability that Sneha sinks a ball is a number not divisible by \(6\) is