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Joe Greedy believes that he has found the location where a Spanish galleon that was transporting a gold shipment worth $10 million sank. He estimates that the probability that he has correctly determined the general area where the shipwreck took place is p. If the treasure is indeed in this area, the probability that he would find it during a dive is q. Dives are independent. Each dive costs c thousands of dollars and Joe has enough money to fund N dives.
Question: Use Bayes’ theorem to determine p_k, the conditional probability that the treasure be in the area given that k unsuccessful dives have been made previously.