Answer:
Probability that the fifth ball selected is red = 0.705
Step-by-step explanation:
Let
= Number of red balls after the 4th turn
⇒
∈ { 0, 1, 2 }
Then,
P = ![\left[\begin{array}{ccc}0.8&0.2&0\\0.1&0.8&0.1\\0&0.2&0.8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.8%260.2%260%5C%5C0.1%260.8%260.1%5C%5C0%260.2%260.8%5Cend%7Barray%7D%5Cright%5D)
⇒![P^{4} = \left[\begin{array}{ccc}0.487&0.435&0.776\\0.218&0.565&0.218\\0.776&0.435&0.487\end{array}\right]](https://tex.z-dn.net/?f=P%5E%7B4%7D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0.487%260.435%260.776%5C%5C0.218%260.565%260.218%5C%5C0.776%260.435%260.487%5Cend%7Barray%7D%5Cright%5D)
Now,
P(5th ball is red |
= 2 ) = 0.
+ 
= 
= 0.705
∴ we get
Probability that the fifth ball selected is red = 0.705
The answer is -3 because you are subtracting 3 every time.
2 x 37 = 74
40 x 37 = 1480
74 + 1480 = 1554
Total 4 decimals so it's 0.1554
Answer
1st box: 4
2nd box : 4