LUMS marketing office advertised two positions for their department. From previous data, it is known that: For each female applicant, the probability that she qualifies in her interview is 0.67. And, for each male, the probability that he qualifies in his interview is 0.63. A hiring requirement by the marketing office is that both positions be filled by candidates of the same gender (both males or both females). To satisfy this requirement, they used the following strategy: They categorized all applicants into two groups: females and males. Then, they chose one of the two groups. They were 4 times more likely to pick the female group than the male group. (a) What is the probability the male group is chosen? Your answer correct up to FOUR decimal places. (b) The office invited two candidates from the chosen group. What is the probability that both of them will clear the interview (i.e., qualify for the positions)? Your answer correct up to FOUR decimal places. (c) The office invited two candidates from the chosen group. What is the probability that exactly one of them will clear the interview (i.e., qualify for the positions)? Your answer correct up to FOUR decimal places. (d) Given that two invited applicants both clear the interview, what is the probability that they were females? Your answer correct up to FOUR decimal places.
LUMS marketing office advertised two positions for their department. From previous data, it is known that: For each female applicant, the probability that she qualifies in her interview is 0.67. And, for each male, the probability that he qualifies in his interview is 0.63. A hiring requirement by the marketing office is that both positions be filled by candidates of the same gender (both males or both females). To satisfy this requirement, they used the following strategy: They categorized all applicants into two groups: females and males. Then, they chose one of the two groups. They were 4 times more likely to pick the female group than the male group. (a) What is the probability the male group is chosen? Your answer correct up to FOUR decimal places. (b) The office invited two candidates from the chosen group. What is the probability that both of them will clear the interview (i.e., qualify for the positions)? Your answer correct up to FOUR decimal places. (c) The office invited two candidates from the chosen group. What is the probability that exactly one of them will clear the interview (i.e., qualify for the positions)? Your answer correct up to FOUR decimal places. (d) Given that two invited applicants both clear the interview, what is the probability that they were females? Your answer correct up to FOUR decimal places.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Contingency Table
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Transcribed Image Text:LUMS marketing office advertised two positions for their department.
From previous data, it is known that: For each female applicant, the probability that she qualifies in her interview is 0.67. And, for each male, the probability that
he qualifies in his interview is 0.63.
A hiring requirement by the marketing office is that both positions be filled by candidates of the same gender (both males or both females). To satisfy this
requirement, they used the following strategy:
They categorized all applicants into two groups: females and males. Then, they chose one of the two groups. They were 4 times more likely to pick the female
group than the male group.
(a) What is the probability the male group is chosen? Your answer
correct up to FOUR decimal places.
(b) The office invited two candidates from the chosen group. What is the probability that both of them will clear the interview (i.e., qualify for the positions)?
Your answer
correct up to FOUR decimal places.
(c) The office invited two candidates from the chosen group. What is the probability that exactly one of them will clear the interview (i.e., qualify for the
positions)? Your answer
correct up to FOUR decimal places.
(d) Given that two invited applicants both clear the interview, what is the probability that they were females? Your answer
up to FOUR decimal places.
correct
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