Suppose Bus2 190 has 25 students enrolled. Assume that there is a 5% change that each student will be interested in their phone at some point in the class. Then, there is a 70% chance that Dr. Yagci Sokat can catch a student when she/he is on her/his phone. If Dr. Yagci Sokat catches you, she will ask you to share an embarrassing story about yourself (or she will ask your friends to share one about you). Dr. Yagci Sokat wants to see whether she can hear an embarrassing story or not in a given class day. As a student, you wonder whether you would have to share two or more embarrassing secrets about yourselves in the 30 class long academic semester.

a) From Dr. Yagci Sokat's point, state the distribution. Identify the independent trials process in this description. Specify what a trial is, what a success is, and what the probability of success is.

b) As a student, state the distribution. Identify the independent trials process in this description. Specify what a trial is, what a success is, and what the probability of success is.

c) What is the probability that you would have to share two or more dirty secrets about yourself in 30 class long academic semester?

d) What is the probability that we will not hear an embarrassing story in today's class?

e) Now, Dr Yagci Sokat is very tempted to ask donuts in addition to the embarrassing story if she catches two or more people on their phone in a given day. If this happens the class will get free donuts from the people who were on their phones. What is the probability that the class will receive a free donut on a given day?