Question

The night watchman in a factory cannot guard both the safe in back and the cash register in front. The safe contains $6000, while the register has only $1000. Tonight the guard fears a robbery; the probability that the thief will try the cash register is 0.8 and the probability the thief will try the safe is 0.2. If the guard is not present, the thief will take all the money. If the guard is present, the thief will go away empty handed. Where should the guard be positioned in order to minimize the thief’s gains?

Answer 1

Answer:

The guard should be positioned at the safe

Step-by-step explanation:

The night watchmen should be positioned to guard whichever place gives the highest expected value to the thief.

The expected value of robbing the safe is:

$EV_{s} = \ 6000*0.2\\EV_{s} = \ 1200$

The expected value of robbing the cash register is:

$EV_{r} = \ 1000*0.8\\EV_{r} = \ 800$

Therefore, the guard should be positioned at the safe since it yields a higher expected value to the thief in case he tries to rob it.