30. Consider a simultaneous roll of 21 dice, and a sample space defined as S fn1;...

30. Consider a simultaneous roll of 21 dice, and a sample space defined as S ¼

fðn1; n2; . . . ; n6Þg, where nj denotes the number of dice showing j dots. Develop formulaic or numerical solutions to the following:

(a) What is the probability of the sample point s ¼ ð1; 2; 3; 4; 5; 6Þ?

(b) What is the probability of the event A ¼ fs j n6 ¼ 12 and n3 ¼ 2g? (Hint: Can this event be defined in terms of ðn3; n6; notherÞ with adjusted probabilities?)