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    Can I please have some help on this problem. I have knowledge up to s2 and I'm not sure how to do this problem.
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    (Original post by Johnturner)
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    Can I please have some help on this problem. I have knowledge up to s2 and I'm not sure how to do this problem.
    These facts could be written like this:

    P(alarm triggered | burglary) = 0.95
    P(alarm triggered | no burglary) = 0.01
    P(burglary) = 0.005

    Does this help?

    Also, "Based on previous false alarms..." may indicate that the sample size is small or that the data isn't reliable. But I may be putting too much thought into this - you probably just need to do the maths and not go into too much depth.
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    (Original post by Notnek)
    These facts could be written like this:

    P(alarm triggered | burglary) = 0.95
    P(alarm triggered | no burglary) = 0.01
    P(burglary) = 0.005

    Does this help?

    Also, "Based on previous false alarms..." may indicate that the sample size is small or that the data isn't reliable. But I may be putting too much thought into this - you probably just need to do the maths and not go into too much depth.
    Thank you for this information, Would you do P(A and B) = 0.95*0.05 = 0.00475 so 0.475% (where A is alarm triggered and B is burglary). Im not sure if that is the answer because it doesn't use part B. Am I trying to find P(A and B)? Actually am I supposed to be finding out p(B given A)?
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    (Original post by Johnturner)
    Thank you for this information, Would you do P(A and B) = 0.95*0.05 = 0.00475 so 0.475% (where A is alarm triggered and B is burglary). Im not sure if that is the answer because it doesn't use part B. Am I trying to find P(A and B)?
    No you need to find

    P(burglary | alarm triggered)
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    (Original post by Notnek)
    No you need to find

    P(burglary | alarm triggered)
    Finding it difficult to form an equation here. I know that p(b|a) = p(b and a)/p(a). I found out that p(a and b) is 0.00475. I'm not sure how I will go about finding p(a) here. Ive been trying to manipulate the second equation to get something but it hasn't been successful
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    P(b|a) = p(b)p(a|b) / p(b)p(a|b)*p(b')p(a|b')

    (Bayes' Theorem)
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    (Original post by Johnturner)
    Finding it difficult to form an equation here. I know that p(b|a) = p(b and a)/p(a). I found out that p(a and b) is 0.00475. I'm not sure how I will go about finding p(a) here. Ive been trying to manipulate the second equation to get something but it hasn't been successful
    Hint: P(A and B') + P(A and B) = P(A)

    You can use a Venn Diagram to see this is true.

    Or you could do this all directly using a form of Bayes Theorem but I don't know which probability formulas you know.
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    (Original post by Notnek)
    Hint: P(A and B' + P(A and B) = P(A)

    You can use a Venn Diagram to see this is true.

    Or you could do this all directly using a form of Bayes Theorem but I don't know which probability formulas you know.
    I think it's my fault for trying to do the problem sheet early - Im sure the intended method was using bases theorem which I am yet to learn. However from using that information you have p(A and B') = p(B')*0.01 = 0.00995. Then you have p(a) = 0.00995+0.00475 = 0.00147(1.47%). would this be the solution
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    (Original post by Johnturner)
    I think it's my fault for trying to do the problem sheet early - Im sure the intended method was using bases theorem which I am yet to learn. However from using that information you have p(A and B')= p(B')*0.01 = 0.00995. Then you have p(a) = 0.00995+0.00475 = 0.00147(1.47%). would this be the solution
    You need to find P(b | a) to answer the question.
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    (Original post by Notnek)
    You need to find P(b | a) to answer the question.
    oh yeah. so p(a and b)/p(a) = 0.00475/0.00147 = 3.23 - wouldn't that be 323% or am I making a mistake somewhere
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    (Original post by Johnturner)
    oh yeah. so p(a and b)/p(a) = 0.00475/0.00147 = 3.23 - wouldn't that be 323% or am I making a mistake somewhere
    In your post before this one you said

    0.00995+0.00475 = 0.00147

    But that's not right
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    (Original post by Notnek)
    In your post before this one you said

    0.00995+0.00475 = 0.00147

    But that's not right
    Wow, yeah it's 0.0147, not sure if I should put that down to tiredness or incompetence. May be both. So it would be 32.3%, thank you for your help.
 
 
 
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