Answered: Given the following fictitious data 40%…

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

Given the following fictitious data 40% of all undergraduates at XYZ University are from Florida and
60% from out of state. 22% are freshmen, and 78% are not. Out of all freshmen, 36% are from Florida,
and 64% from out of state. Determine the probability a randomly selected XYZ University undergraduate:
Suggestion: Make a tree diagram with the first branches being freshmen or not.
a) is from Florida and a freshman.

b) is from Florida and not a freshman.
c) is from out of state and not a freshman.

d) is a freshman given the student is from Florida.

Expert Solution

Step 1: Given Information

40% of undergraduates are from Florida (F), and 60% are from out of state (O).
22% of students are freshmen (Fr), and 78% are not (N).
Among freshmen, 36% are from Florida, and 64% are from out of state.

First, let's define the probabilities given in the problem:

$P (Florida) = 0.40$
$P (Out of state) = 0.60$
$P (Freshman) = 0.22$
$P (Not Freshman) = 0.78$
$P (Florida ∣ Freshman) = 0.36$ (probability of being from Florida given the student is a freshman)
$P (Out of state ∣ Freshman) = 0.64$ (probability of being from out of state given the student is a freshman)