Question

Three boys A, B, C are throwing a ball each other. A always throws the ball to B and B always throws the ball to C, but C is just as likely to throw the ball to B as to A. If C was the first person to throw the ball find

Answer 1

Answer:

krishnasahu harami the c will throw the ball to A

iE Krishnasahu BC

Answer 2

Answer:

$\{X_n\}$ is a Markov process.

Step-by-step explanation:

[As the question is incomplete, giving the transition probability matrix of the problem]

Given three boys A, B, C are throwing a ball each other.

A always throws the ball to B

B always throws the ball to C.

C is just as likely to throw the ball to B as to A

The transition probability matrix also called as Markov matrix gives the probabilities of transitions from one state to another in a single time unit.

Each entity is a nonnegative real number representing a probability.

The transition probability matrix of the process of transmitting the ball between the boys is given by

$~~~~~~~~~~~~~~~~~~~~~~~~~X_{n}\\\\\p~=~X_{n-1}\left[\begin{array}{cccc}&A&B&C\\A&0&1&0\\B&0&0&1\\C&\frac{1}{2} &\frac{1}{2}&0\end{array}\right]$

A Markov process is a random process in which the future is independent of the past, given the present.  

States of $X_n$ depends only on the states of $X_{n-1}$, but not on the past states $X_{n-2}, X_{n-3}...$or earlier states.

Therefore, $\{X_n\}$ is a Markov process.