Probability to find treasure

Question

You have a metal detector that will beep 99 times out of 100 if it contains buried treasure within a metre squared. It will also beep 1 time in a 100 if it does not contain buried treasure. I'm searching an island containing John last hidden treasure. You have divided the island up into 1,001 1 metre by 1 metre squares which you plan to test individually. On the first square the metal detector beeps. What is the chance that you've discovered the treasure?

I have no idea how to tackle this problem. Would you like to help me please?

Answer 1

Guide:

Let $B$ denotes the event that the metal detector beeps.

Let $T$ denote the event that there is treassure.

Now apply Bayes rule on $P(T|B)=\frac{P(T)P(B|T)}{P(B)}=\frac{P(T)P(B|T)}{P(T)P(B|T)+P(T^c)P(B|T^c)}$.

You will have to make some assumption, such as the treassure only appears in exactly one of the squares.