Solution
Robert answered on
Dec 23 2021
One way to solve this problem is to consider there to be 8 states - Each of A, B, and C surviving.
Labelling these 8 states by (A, B, C), 0 indicating death and 1 survival, we have
(0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1), (1, 0, 0), 1, 0, 1), (1, 1, 0), (1, 1, 1) for row and column
When we are in any state with A + B + C = 0 or 1, there is no further firing. Thus, we stay in this
statement.
In all other cases, we have transition. In the case where we only have 2 tanks remaining, we
have to use multiplications to see probability of each of the four results. In the case where we
have 3 tanks, we similarly use multiplications, taking into account the probability = 1/2 of firing at
each of the other 2 tanks.
Of course, we start with everyone in state (1, 1, 1)
For the first three states, (0, 0, 0), (0, 0,...