Question

Problem 3: Rick goes to career fair booths in the technology sector for data science jobs (e.g., Facebook, Amazon, IBM, etc.). His likelihood of receiving an off-campus interview invitation after a career fair booth visit depends on how well he did in MIE 263. Especially, an A in MIE 263 results in a probability p=0.95 of obtaining an invitation, whereas a C in MIE 263 results in a probability of p=0.15 of an invitation. (Whether a student will get an invitation is independent on whether he will get an invitation from other firms.) Furthermore, to get an A, a student has to pass all quizzes. The probability that Rick passes any quiz is 0.5. Rick’s performance on each
quiz is independent of his performance on all other quizzes.

c) Assuming that each student visits 5 booths during a typical career fair, find the probability that an A student in MIE 263 will not get an off-campus interview invitation.Similarly, find the probability that a C student in MIE 263 will get an invitation during a typical career fair.
d) Determine the probability that Rick will pass exactly two out of the first four quizzes.
e) Determine the probability that the third quiz Rick takes is the first one that he fails.
f) Given that Rick failed four times in his first eight quizzes, determine the conditional
probability that his fifth failure will occur on the eleventh quiz.
g) Determine the probability that Rick’s second failure occurs on his fifth quiz.

Answer 1

In the 1st part of the question we assume that a student either A or C can obtain only one interview invitation from a career booth. So out of 5 booths one student can obtain at-most 5 invitations with certain probability and getting invitation from a booth is independent of other booths. Similarly the outcome of the quizzes are also independent of each other for Rick. So both the no interview invitation and no of failure/success in quizzes follow Binomial distribution with certain parameters.The step by step explanations are given in the images...