Question

In order for any SIPR access to occur, there must be adequate power generation. The Brigade requires 160 kW of power at all times for full operation of their Tactical Operations Center (TOC). They deploy two 100 kW generators, five 60 kW generators, and four 30 kW generators for this purpose and any number of them can be used at any time to achieve the required power level. However, the transportation contractor reports that an accident damaged seven of these 11 generators during transit to theater. The contractor was not able to specify which ones were damaged. (20 points) Calculate the probability the undamaged generators will provide the required 160 kW.

Answer 1

Total no. Of ways in which  7 generators could be damaged = ¹¹C_{7 = 330}

To achieve required power level, the sum of the capacity of 4 remaining undamaged generators have to be equal to OR greater than 160 kW.

4 undamaged generators will fail to supply required power if all 4 of them are 30W generators

or

one 60W and three 30W generators are left undamaged.

In all remaining, the power requirement will be met easily.

Required probability = 1- ( ⁴C₄ + ⁵C_{1 *}  ⁴C₃ )/330 = 1- 21/330 = 309/330 = 0.9363