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Company A will default with probability .01, company B will default with probability .05, and company...

Company A will default with probability .01, company B will default with probability .05, and company C will default with probability .09. I will buy a bond of company A with probability .5, I will buy a bond of company B with probability .3, and I will buy a bond of company C with probability .2. Given that the bond that I bought defaults, what is the probability that the bond was of Company A?

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