 # Probability question

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.php?p_faqid=170&p_created=1179447247&p_sid=ikWsYdLi&p_accessibility=0&p_lva=&p_sp=cF9zcmNoPSZwX3NvcnRfYnk9JnBfZ3JpZHNvcnQ9JnBfcm93X2NudD0xNyZwX3Byb2RzPSZwX2NhdHM9JnBfcHY9JnBfY3Y9JnBfc2VhcmNoX3R5cGU9YW5zd2Vycy5zZWFyY2hfbmwmcF9wYWdlPTE*&p_li=&p_topview=1 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® = P(RI) + P(RI’) = 0.57 [Rising interest rates] P(R’) = 0.43 [Non rising interest rates] P(I|R) = P(IR) / P® =0.6842 [Inflation given rising interest rates]

cpk123, Thanks. Dreary