Question
vaue: 10.00 points You did not receis An analyst estimates that the probability of dofault on a seven-year AA-rated bond is 0.49, while that on a seven-year A-rated bond is 0.51. The probability that they will both default is 0.216 a. What is the probability that at least one of the bonds defaults? (Round your answer to 2 decimal places.) b. What is the probabiity that neither the seven-year AA-rated bond nor the seven-year A-rated bond defaults? (Round your answer to 2 decimal places) c. Given that the seven-year AA-rated bond defaults, what is the probability that the seven-year A-rated bond also defaults? (Round your answer to 2 declmal places.) References eBook & Resources Lsaming Objsctive 04-06 Ojstinguan betwoan independer Learning Objective: 04-04 Calculate and interpret the probability that at least one af two events will occur Worksheet Learning Objectve: 04-05 Calculate and interpret a conditional probablity and apply the multiplication rule Difficulty: 3 Hard MacBook Air
Explanation / Answer
P( default on Aa) = .49
P( default on A) = .51
P( both default) = .26
a. P( defaults on atleast one) =
P( default on Aa)+P( default on A)-P( default on both)
= .49+.51-.26
=.74
b.P( neither of them defaults)
= 1-P( defaults on atleast one)
= 1-.74
= .26
c P( given he defaults on AA, prob of defaulting on A)
= .26/.49
= .531
