Final answer:
The complement of event E, denoted E^C, consists of outcomes not in E. For the given sample space S, E^C consists of {10, 20, 21}. The probability of E^C, P(E^C), is 1/4 or 0.25.
Step-by-step explanation:
The student's question pertains to a probability experiment where a sample space S and an event E are defined. The student is asked to determine the outcome of the complement of the event E (denoted as EC) and calculate the probability P(EC).
To answer the student's question:
The sample space S is {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21}.
Event E is {11, 12, 13, 14, 15, 16, 17, 18, 19}, which contains the outcomes from 11 to 19.
The complement of an event EC consists of all the elements in S that are not in E.
The outcomes in EC are {10, 20, 21}.
To find P(EC), we can use the formula P(A) = number of outcomes in A / number of outcomes in S.
Thus, P(EC) = 3/12 = 1/4 or 0.25.