Question

The Search Problem - An enemy force is known to be hiding in one of twenty possible locations. General Staff orders a search to be made by picking a site at random, inspecting it, then picking the next site to be inspected at random from among the remaining sites and so on. After fifteen sites have been inspected, the search is still unsuccessful. The General Staff begins to believe that the enemy has somehow vanished. Is this belief justified? What if there were two enemy groups?

Answer 1

As above 15 sites have been inspected out of 20 sites and The General Staff begins to believe that the enemy has somehow vanished.

Then, it is not believe justified as 5 sites are still remain to inspect and the probability of getting enemy force is still valid .

So, until all the 20 possible locations are not inspected till it is not justified to believe that the enemy has somehow vanished.

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If there were two enemy groups then

they can choose any two possible locations for hiding in   $\binom{20}{2}$ ways and

The General Staff should also orders two teams for searching locations simultaneously .As the number of enemies will also increase so, with respect to this search team should also increase their numbers .