# [Help]Probability with bayes's theorem

Probability theory and statistics

### [Help]Probability with bayes's theorem

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.

hiensteve

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Joined: Mon Mar 04, 2013 7:25 pm
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### Re: [Help]Probability with bayes's theorem

$p_k$
$= P(\text{Treasure} | \text{k fails})$
$= \frac{P(\text{k fails} | \text{Treasure})P(\text{Treasure})}{P(\text{k fails})}$
$= \frac{P(\text{k fails} | \text{Treasure})P(\text{Treasure})}{P(\text{k fails} | \text{Treasure})P(\text{Treasure})+P(\text{k fails} | \text{No treasure})P(\text{No treasure})}$
$= \frac{(1-q)^k p}{(1-q)^k p + (1-p)}$.

Hope that helps,

R. Baber.

Guest

### Re: [Help]Probability with bayes's theorem

Thanks a lot,
I already did similarly, however, here i did:
pk= [pq.(1-q)]^k/([pq.(1-q)]^k+[(1-p.q)] )
The difference here is only about i putted p.q instead of p only, because here the general area should be considered for both probability of existence of treasure and probability of finding the treasure,

hiensteve

Posts: 2
Joined: Mon Mar 04, 2013 7:25 pm
Reputation: 0

### Re: [Help]Probability with bayes's theorem

You are wrong.

pq is the probability there is treasure and you find it, I don't really understand why you think this term appears in the equation.
The question asks for the probability that there is treasure given there has been k failed dives. If the question was what is the probability that there is treasure given there were k failed dives and one dive which found treasure, then the answer is obviously 1.

R. Baber.

Guest