Please show solutions and explain steps If she made the last free throw, then her probability of making the next one is 0.7. On the other hand, if she missed the last free throw, then her probability of making the next one is 0.2.Assume that **state 1** is Makes the Free Throw and that **state 2** is Misses the Free Throw.1. Find the transition matrix for this Markov process. \[ P = \begin{bmatrix} \, \boxed{} & \boxed{} \, \\ \, \boxed{} & \boxed{} \, \end{bmatrix} \]2. Find the two-step transition matrix \(P(2)\) for this Markov process. \[ P(2) = \begin{bmatrix} \, \boxed{} & \boxed{} \, \\ \, \boxed{} & \boxed{} \, \end{bmatrix} \]3. If she makes her first free throw, what is the probability that she makes the third one? \[ \boxed{} \]3. If she misses her first free throw, what is the probability that she makes the third one? \[ \boxed{} \]

Given that state 1 is Makes the Free Throw and state 2 is Misses the Free Throw. if she made the last free throw, then her probability of making the next one is 0.7. if she missed the last free throw, then her probability of making the next one is 0.2. 1. If she made the last free throw, then her probability of missing the next one=1-0.7=0.3 If she missed the last free throw, then her probability of missing the next one=1-0.2=0.8 The transition matrix for this Markov process is 1 2P=120.70.30.20.82. The two-step transition matrix P(2) for this Markov process P2=P2=0.70.30.20.8×0.70.30.20.8=0.7×0.7+0.3×0.20.7×0.3+0.3×0.80.2×0.7+0.8×0.20.2×0.3+0.8×0.8=0.550.450.30.73. Let P be her second throw results, then P(2) denote her third throw results. If she makes her first free throw, the probability that she makes the third one, P112=0.55 If she misses her first free throw, the probability that she makes the third one, P212=0.3