[Help]Probability with bayes's theorem

Probability theory and statistics

[Help]Probability with bayes's theorem

Postby hiensteve » Mon Mar 04, 2013 7:28 pm

Please help with the question. Thank you guys a lot in advance.

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

Re: [Help]Probability with bayes's theorem

Postby Guest » Tue Mar 05, 2013 4:48 am

[tex]p_k[/tex]
[tex]= P(\text{Treasure} | \text{k fails})[/tex]
[tex]= \frac{P(\text{k fails} | \text{Treasure})P(\text{Treasure})}{P(\text{k fails})}[/tex]
[tex]= \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})}[/tex]
[tex]= \frac{(1-q)^k p}{(1-q)^k p + (1-p)}[/tex].

Hope that helps,

R. Baber.

Guest
 

Re: [Help]Probability with bayes's theorem

Postby hiensteve » Tue Mar 05, 2013 11:34 pm

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,
Pls advise if it's wrong,

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

Re: [Help]Probability with bayes's theorem

Postby Guest » Wed Mar 06, 2013 5:16 am

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
 


Return to Probabilities and Statistics



Who is online

Users browsing this forum: No registered users and 1 guest

cron