Question

It’s believed that a treasure on a sunken wreck will be in a certain sea area...

It’s believed that a treasure on a sunken wreck will be in a certain sea area with probability p = 0.4. A search in that area will detect the wreck with probability d = 0.9 if it’s there. What’s the probability of the treasure being in the area given a search didn’t find anything?

Homework Answers

Answer #1

Let T be the event that the treasure is there.

In case there is no treasure, test cannot be positive, hence NA.

True Treasure
No treasure Treasure
P(T')=0.6 P(T)=0.4
Test positive Test negative Test positive Test negative
NA NA 0.9 0.1
NA NA 0.36 0.04

Given that there is treasure the probability that the wreck will detect - 0.90

hence the probability that the wreck will not detect the grease = 0.10

Hence probability of the treasure being in the area given a search didn’t find anything = 0.1 * 0.4 = 0.04

ANS = 0.04

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