Exercise 8.1 Bickel et al. [1975] report on gender biases for graduate admissions at UC Berkeley. This example is based on that case, but the numbers are fictional. There are two departments, which we will call dept#1 and dept#2 (so Dept is a random variable with values dept#1 and dept#2) which students can apply to. Assume students apply to one, but not both. Students have a gender (male or fe- male), and are either admitted or not. Consider the table of the percent of students in each category of Figure 8.33 (on the next page). In the semantics of possible worlds, we will treat the students as possible worlds, each with the same measure. (a) What is P(Admitted=true | Gender=male)? What is P(Admitted=true | Gender=female)? Which gender is more likely to be admitted?

Exercise 8.1 Bickel et al. [1975] report on gender biases for graduate admissions at UC Berkeley. This example is based on that case, but the numbers are fictional. There are two departments, which we will call dept#1 and dept#2 (so Dept is a random variable with values dept#1 and dept#2) which students can apply to. Assume students apply to one, but not both. Students have a gender (male or fe- male), and are either admitted or not. Consider the table of the percent of students in each category of Figure 8.33 (on the next page). In the semantics of possible worlds, we will treat the students as possible worlds, each with the same measure. (a) What is P(Admitted=true | Gender=male)? What is P(Admitted=true | Gender=female)? Which gender is more likely to be admitted?

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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Question

100%

How should this problem be set up? Specifically the denominator. I'm NOT looking for the answer, so please don't reject my question again.

Dept
Gender Admitted Percent
dept#1 male
true
32
dept#1 male
false
18
dept#1 female true
7
dept#1 female false
3
dept#2 тale
true
dept#2 male
false
14
dept#2 female true
7
dept#2 female false
14
Figure 8.33: Counts for students in departments

Exercise 8.1 Bickel et al. [1975] report on gender biases for graduate admissions
at UC Berkeley. This example is based on that case, but the numbers are fictional.
There are two departments, which we will call dept#1 and dept#2 (so Dept is
a random variable with values dept#1 and dept#2) which students can apply to.
Assume students apply to one, but not both. Students have a gender (male or fe-
male), and are either admitted or not. Consider the table of the percent of students
in each category of Figure 8.33 (on the next page).
In the semantics of possible worlds, we will treat the students as possible
worlds, each with the same measure.
(a) What is P(Admitted=true | Gender=male)?
What is P(Admitted=true | Gender=female)?
Which gender is more likely to be admitted?

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