When rolling 4 dice, the minimum sum is 4 and the maximum is 24. To achieve a sum of 22 or more, the possible target sums are 22, 23, and 24. The number of combinations for these sums are 10, 4, and 1 respectively, giving 15 total favorable outcomes out of 1296. The probability is 15 divided by 1296, which simplifies to 5/432.