Explanation
The probabilities of default of the two bonds are independent (as indicated by a zero default correlation). The various possible states of the portfolio are as follows:
First bond defaults, and the second does not: Probability * Loss = 0.03*0.92* $50m = $1.38m Second bond defaults, and the first does not: Probability * Loss = 0.97*0.08 * $50m = $3.88m Both bonds default: Probability * Loss = 0.03*0.08 * $100m = $0.24m Thus total expected loss on this portfolio = $5.5m. Since recovery rates are not provided, those should be assumed to be zero.
There is an easier way to solve this as well: default correlation does not affect expected losses, but their volatility. You can calculate the expected losses of the two bonds and add them up, ie, $50m*0.03+ $50m
*0.08 = $5.5m