Probability question

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There is a 45% probability of rising interest rates with no inflation and a 45+65%=110% probability of rising interest rates with inflation. What is the probability of inflation when interest rates are rising, given a 60% chance of inflation?
This somehow doesn’t look straightforward!
Could you explain your answer?
Dreary
 
Please look at the Errata. I remember this was a Stalla question for which I had raised the errata.
Revised question:
1/5/07
2
101
Question #9 should read as: “There is a 45% probability of rising interest rates with no inflation and a 65% probability of rising interest rates with inflation.”
FYI.
Location of errata:
http://stallakb.custhelp.com/cgi-bin/stallakb.cfg/php/enduser/std_adp.ph...
Regards
CP
 
110% probability… I doubt anybody can explain that.
What makes the 45 + 65 =110 % ???
 
“There is a 45% probability of rising interest rates with no inflation and a 45+65%=110% probability of rising interest rates with inflation”
You shouldn’t add 45% and 65% together because one is given no inflation while the the latter is given inflation.
R = interest rate rise
I = Inflation
P(R|I) = 0.65 [Rising Interest rates given inflation already occurs]
P(R’|I) = 0.35 [Non rising interest rates given inflation already occurs]
P(R|I’) = 0.45 [Rising interest rates given no inflation already occurs]
P(R’|I’) = 0.55 [Non rising interest rates given no inflation already occurs]
P(I) = 0.6 [Inflation]
P(I’) = 0.4 [No inflation]
Then we can workout
P(RI) = P(R|I) * P(I) = 0.39 [Rising interest rates and inflation]
P(R’I) = 0.21 [Non rising interest rates and inflation]
P(RI’) = 0.18 [Rising interest rates and no inflation]
P(R’I’) = 0.22 [Non rising interest rates and no inflation]
Thus
P(R) = P(RI) + P(RI’) = 0.57 [Rising interest rates]
P(R’) = 0.43 [Non rising interest rates]
P(I|R) = P(IR) / P(R) =0.6842 [Inflation given rising interest rates]
 
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