The probability of default for credit scores of 650 or below, totaling 90 defaulters out of 630 loan recipients, the probability is 0.14, representing a 14% likelihood.
Certainly, let's break down the calculation step by step:
1. Given Information:
- Defaulters in three credit score categories: 30 + 30 + 30 = 90 individuals.
- Total loan recipients in the same categories: 120 + 240 + 270 = 630 individuals.
2. Probability Calculation:
- Probability is defined as the number of defaulters divided by the total number of loan recipients.
- Probability of default = Number of defaulters / Total number of loan recipients.
3. Substitute Values:
- Substitute the given counts into the probability formula.
- Probability of default = 90 / 630.
4. Simplify:
- Simplify the fraction to obtain the probability.
- Probability of default = 0.14 (rounded to two decimal places).
In summary, the step-by-step calculation involves identifying the number of defaulters, determining the total number of loan recipients, applying the probability formula, and simplifying to derive the final probability of loan default, which in this case is 0.14.