Question

help number 1

1. Ezra is entering her senior year of college and would like to pursue a master's degree in computer science immediately following her graduation. She has aready submitted applications to all five of her top choices for grad school MIT,Stanford, Carnegie Mellon, UC Berkeley, and USC. Additionally, she has submitted applications to several backup schools. In the course of researching the programs at her top schools, she noted each programs acceptance rate, which are displayed in the table below School MIT Stanford Carnegie Mellon UC Berkeley USC Acceptance Rate 15% 12% 19% 24% 31% a. What is the probability that Ezra is accepted into all five of these programs? Round your answer to 4 decimals. b. What is the probability that she is accepted into none of these programs? Round your answer to 4 decimals 2 points) c. What is the probability that she is only accepted into Carnegie Mellon? Round your answer to 4 2 points d. Does this table satisfy the conditions required to constitute a MECE distribution? Explain your reasoning for each of the conditions

Answer 1

a) P(Ezra is accepted into all five of these programs) = 0.15 x 0.12 x 0.19 x 0.24 x 0.31

= 0.00025

b) P(she is accepted into none of these programs) = (1 - 0.15) x (1 - 0.12) x (1 - 0.19) x (1 - 0.24) x (1 - 0.31)

= 0.85 x 0.88 x 0.81 x 0.76 x 0.69

= 0.31772

c) P(She is accepted only in Carnegie Mellon) = (1 - 0.15) x (1 - 0.12) x 0.19 x (1 - 0.24) x (1 - 0.31)

= 0.07453

d) It is possible for her to get accepted by multiple programs.Thus, the distribution here is not mutually exclusive and collectively exclusive. Therefore this doesn't satisfy the conditions for MECE distribution.