Question

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 atrandom, inspecting it, then picking the next site to be inspected at random fromamong the remaining sites and so on. After fifteen sites have been inspected, thesearch 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

Answer and Explanation:

No, the the belief of the general staff is not justified.

This can be explained as the inspection of the 15 locations out of 20 locations turned out to be abortive, there are still 5 sites left to be inspected.

Therefore, only after the simultaneous inspection of all the 20 sites, the belief would be justified and not before that.

If there were two enemy groups then they could chose the sites in
`{20}^C_(2)`, i.e., 190 ways to hide.

Therefore, the General Staff should also command for 2 simultaneous inspection.

Since, there is an increase in the number of enemies, the Inspection team should also expand and increase their team mates.