Q2 A triangle ABC is drawn on a plane, and a ball is placed on vertex A. A dice is rolled, and the ball is moved according to the following rules: (i) when the ball is on A, if the number on the dice is 1 the ball is moved to B, otherwise it stays on A; (ii) when the ball is on B, if the number on the dice is less than or equal to 4 the ball is moved to C, otherwise it stays on B. If the ball is moved to C, the trials are stopped. We are to find the probability that the ball is moved to C within 4 rolls of the dice. (1) The probability that the ball is moved to C on the second roll of the dice is $\frac { 1 } { \mathbf{N} }$ (2) The probability that the ball is moved to C on the third roll of the dice is $\frac{\mathbf{O}}{\mathbf{PQ}}$ (3) The probability that the ball is moved to C on the fourth roll of the dice is $\frac{\mathbf{RS}}{\mathbf{TUV}}$ Therefore, find the probability that the ball is moved to C within 4 rolls of the dice.
Q2 A triangle ABC is drawn on a plane, and a ball is placed on vertex A. A dice is rolled, and the ball is moved according to the following rules:\\
(i) when the ball is on A, if the number on the dice is 1 the ball is moved to B, otherwise it stays on A;\\
(ii) when the ball is on B, if the number on the dice is less than or equal to 4 the ball is moved to C, otherwise it stays on B.
If the ball is moved to C, the trials are stopped.
We are to find the probability that the ball is moved to C within 4 rolls of the dice.\\
(1) The probability that the ball is moved to C on the second roll of the dice is $\frac { 1 } { \mathbf{N} }$\\
(2) The probability that the ball is moved to C on the third roll of the dice is $\frac{\mathbf{O}}{\mathbf{PQ}}$\\
(3) The probability that the ball is moved to C on the fourth roll of the dice is $\frac{\mathbf{RS}}{\mathbf{TUV}}$
Therefore, find the probability that the ball is moved to C within 4 rolls of the dice.