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- Solutions
1 Situation:
The High School and Beyond data is from a large-scale longitudinal study
conducted by the National Opinion Research Center (1980) under contract with the
National Center for Education Statistics.
Below is a table representing a sample of 100
students from this data that includes the student’s gender and whether the high school
they attended was public or private.
Let A denote the subset of these 100 subjects that
the student is Female, so the event A = {Female}. Similarly define event B as the student
attended a Public high school, so the event B = {Public}.
. The following 2x2 table
classifies each student according to gender and school type.
Public
Private
Total
Female
38
7
45
Male
46
9
55
Total
84
16
100
For example, the table reveals that 38 students were both Female and attended a Public
high school, so:
P(A ∩ B) = 38/100 = 0.38 (read “the probability of A and B is 0.38)).
a.
Fill in the marginal
totals of the table (the row and column totals). From these totals
determine the probability that the student is Female and also the probability the student
attended a Public high school. Answer the following placing the proper event notation
(e.g. A, B) in the ( ).
P(Female) = P(
A
) =
.45
P(Public) = P(
B
) =
.84
b.
Translate the following events into set notation using the symbols A and B,
complement, union, intersection. Also give the probability of the event as determined
from the table above. Fill in the table below with these values. {If you cannot construct
the symbol ∩, just use & or copy and paste} Lastly, draw a Venn diagram (on scratch
paper, but you need not submit it) showing the events of Female, Public, and both Female
and Public.
The first one is completed for you.
Event in words

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