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?
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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