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# Statistics Problem watch

1. 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.
2. (Original post by Johnturner)

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.
3. (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)?
4. (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)
5. (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
6. P(b|a) = p(b)p(a|b) / p(b)p(a|b)*p(b')p(a|b')

(Bayes' Theorem)
7. (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.
8. (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
9. (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.
10. (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
11. (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
12. (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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