Answer:
6 out of 7 6/7
Step-by-step explanation:
Mmm statistics at its best, okay lets go.
So I’m assuming this is a 7 sided die or something along those lines.
So, if you could land on any other value EXCEPT for seven, since six values are before, it would be a 6 out of 7 chance to not land on a 7.
Answer:
19/100 or 5/26
Step-by-step explanation:
i think
Answer:
-25/12
Step-by-step explanation:
Hope this helps
Answer:
The stationary matrix is:
S = [0.2791, 0.7209]
Step-by-step explanation:
The transition matrix, <em>P</em> is:
![P=\left[\begin{array}{cc}0.38&0.62\\0.24&0.76\end{array}\right]](https://tex.z-dn.net/?f=P%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.38%260.62%5C%5C0.24%260.76%5Cend%7Barray%7D%5Cright%5D)
The stationary matrix S for the transition matrix P would be obtained by computing <em>k</em> powers of <em>P</em> until all the two rows of <em>P</em> are identical.
Compute P² as follows:
![P^{2}=\left[\begin{array}{cc}0.38&0.62\\0.24&0.76\end{array}\right]\times \left[\begin{array}{cc}0.38&0.62\\0.24&0.76\end{array}\right]](https://tex.z-dn.net/?f=P%5E%7B2%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.38%260.62%5C%5C0.24%260.76%5Cend%7Barray%7D%5Cright%5D%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.38%260.62%5C%5C0.24%260.76%5Cend%7Barray%7D%5Cright%5D)
![=\left[\begin{array}{cc}0.2932&0.7068\\0.2736&0.7264\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.2932%260.7068%5C%5C0.2736%260.7264%5Cend%7Barray%7D%5Cright%5D)
Compute P³ as follows:
![P^{3}=P^{2}\times P](https://tex.z-dn.net/?f=P%5E%7B3%7D%3DP%5E%7B2%7D%5Ctimes%20P)
![=\left[\begin{array}{cc}0.2932&0.7068\\0.2736&0.7264\end{array}\right]\times \left[\begin{array}{cc}0.38&0.62\\0.24&0.76\end{array}\right]\\\\=\left[\begin{array}{cc}0.2810&0.7190\\0.2783&0.7217\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.2932%260.7068%5C%5C0.2736%260.7264%5Cend%7Barray%7D%5Cright%5D%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.38%260.62%5C%5C0.24%260.76%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.2810%260.7190%5C%5C0.2783%260.7217%5Cend%7Barray%7D%5Cright%5D)
Compute P⁴ as follows:
![P^{4}=P^{3}\times P](https://tex.z-dn.net/?f=P%5E%7B4%7D%3DP%5E%7B3%7D%5Ctimes%20P)
![=\left[\begin{array}{cc}0.2810&0.7190\\0.2783&0.7217\end{array}\right]\times \left[\begin{array}{cc}0.38&0.62\\0.24&0.76\end{array}\right]\\\\=\left[\begin{array}{cc}0.2793&0.7207\\0.2790&0.7210\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.2810%260.7190%5C%5C0.2783%260.7217%5Cend%7Barray%7D%5Cright%5D%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.38%260.62%5C%5C0.24%260.76%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.2793%260.7207%5C%5C0.2790%260.7210%5Cend%7Barray%7D%5Cright%5D)
Compute P⁵ as follows:
![P^{5}=P^{4}\times P](https://tex.z-dn.net/?f=P%5E%7B5%7D%3DP%5E%7B4%7D%5Ctimes%20P)
![=\left[\begin{array}{cc}0.2793&0.7207\\0.2790&0.7210\end{array}\right]\times \left[\begin{array}{cc}0.38&0.62\\0.24&0.76\end{array}\right]\\\\=\left[\begin{array}{cc}0.2791&0.7209\\0.2791&0.7209\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.2793%260.7207%5C%5C0.2790%260.7210%5Cend%7Barray%7D%5Cright%5D%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.38%260.62%5C%5C0.24%260.76%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.2791%260.7209%5C%5C0.2791%260.7209%5Cend%7Barray%7D%5Cright%5D)
For <em>k</em> = 5, we get both the rows identical.
The stationary matrix is:
S = [0.2791, 0.7209]