Final answer:
In this question, we are given the number of students who tried out for a school play and the number of students who did not get a role. We can calculate the number of students who we expect to attend the festivities, the probability that at most four students will attend, and the probability that more than two students will attend.
Step-by-step explanation:
In this question, we are given that there can be only 12 students in the next school play. Let t represent the number of students who tried out for the play and the number of students who tried out but did not get a role is 42. In order to find the number of students who we expect to attend the festivities (part d), we can subtract the number of students who did not get a role from the total number of students who tried out. Therefore, the number of students who we expect to attend the festivities is t - 42.
To find the probability that at most four students will attend (part e), we need to consider the total number of students who can attend, which is 12. We can then calculate the probability by dividing the number of students who will attend (0 to 4) by the total number of students (12). The probability is the sum of these individual probabilities.
To find the probability that more than two students will attend (part f), we need to consider the total number of students who can attend, which is 12. We can then calculate the probability by subtracting the probability of the complement event (less than or equal to two students) from 1. The probability is the sum of these individual probabilities.