>>12843244One interpretation:
Roll 2 die simultaneously that total 27 and do that twice. For the 1st 2-die roll, the combinations that give 27 are several. Each combination, such as 12+15, is a JOINT probability of (1st die=x) AND (2nd die=y), so we apply JOINT probability to each combination.
P(7+20) = 1/20 * 1/20 =1/400
P(8+19) =1/20 * 1/20 =1/400
P(9+18) = 1/20 * 1/20 =1/400
P(10+17) = 1/20 * 1/20 =1/400
P(11+16) = 1/20 * 1/20 =1/400
P(12+15) = 1/20 * 1/20 =1/400
P(13+14) = 1/20 * 1/20 =1/400
P(14+13) = 1/20 * 1/20 =1/400
P(15+12) = 1/20 * 1/20 =1/400
P(16+11) = 1/20 * 1/20 =1/400
P(17+10) = 1/20 * 1/20 =1/400
P(18+9) = 1/20 * 1/20 =1/400
P(19+8) = 1/20 * 1/20 =1/400
P(20+7) = 1/20 * 1/20 =1/400
The above die pairs make up a set of ALTERNATIVES (OR condition) that yield the desired “2-die roll=27”. As listed above, there are 14 ALTERNATIVES that yield “2-die roll=27” The TOTAL probability for ALTERNATIVES is the SUM of probabilities for all ALTERNATIVES, or
TOTAL probability for ALTERNATIVES =
= 1/400 * 14 = 0.035 TOTAL probability for “roll 27”
For “2-die roll=27” two times in a row are 2 independent occurrences, a JOINT probability, so we use the PRODUCT for each occurrence,
0.035 * 0.035 = 0.001225 ~ TOTAL probability for “2-die roll=27” two times in a row
