The Altman z-score (Links to an external site.) is a commonly used metric to estimate likelihood of default, based on a combination of financial ratios. If the score for a company is less than 1.81, it is considered to be at high risk of default over the next year. In testing this metric against historical data from 1980 to 2000, you find the following results:

P(at risk | no default) = 0.05

P(not at risk) = 0.85

P(default) = 0.06

What is P(default | at risk), the probability that a company defaults, given that it is "at risk" according to the z-score?

Enter answer as a percentage, accurate to two decimal places.

Based on your result, think whether this looks like a useful default prediction metric.

Hint: First find P(at risk | default), then apply Bayes' rule.