Step-by-step Solution:

The total number of caps: \[ 2 + 4 + 5 + 1 = 12 \] The number of ways for selecting four caps: \[ ^{12}C_4 \] The total number of caps other than green: \[ 12 - 5 = 7 \] The number of ways for selecting four caps other than green: \[ ^{7}C_4 \] The probability of selecting four caps and none of them are green \( P(A') \): \[ P(A') = \frac{\text{Number of ways for selecting four caps other than green}}{\text{Number of ways for selecting four caps}} \] \[ P(A') = \frac{^{7}C_4}{^{12}C_4} \] \[ P(A') = \frac{\frac{7!}{(7-4)!4!}}{\frac{12!}{(12-4)!4!}} \] \[ P(A') = \frac{7!}{(7-4)!4!} \times \frac{(12-4)!4!}{12!} \] \[ P(A') = \frac{7}{99} \]