The question is a conditional probability problem. To determine the probability that a randomly selected late mortgage is a subprime mortgage, we follow these steps:

1. Calculate the total number of mortgages that are late:

   • There are 200 subprime mortgages that are late and 48 prime mortgages that are late.
   • Total late mortgages = 200 (subprime late) + 48 (prime late) = 248.

2. Calculate the total number of mortgages in the portfolio:

   • There are 1,000 subprime mortgages and 600 prime mortgages.
   • Total mortgages = 1,000 (subprime) + 600 (prime) = 1,600.

3. Calculate the probability that a randomly selected mortgage is late:

   • P(Mortgage is late) = Total late mortgages / Total mortgages
   • P(Mortgage is late) = 248 / 1,600 = 15.5%.

4. Calculate the probability that a randomly selected mortgage is both subprime and late:

   • P(Subprime mortgage and late) = Number of subprime late mortgages / Total mortgages
   • P(Subprime mortgage and late) = 200 / 1,600 = 12.5%.

5. Use the conditional probability formula to find the probability that a mortgage is subprime given that it is late:

   • P(Subprime mortgage | Mortgage is late) = P(Subprime mortgage and late) / P(Mortgage is late)
   • P(Subprime mortgage | Mortgage is late) = 12.5% / 15.5% = 0.81 or 81%.

Therefore, the probability that a randomly selected late mortgage from the portfolio is a subprime mortgage is 81%. The correct answer is D.