Answered: Last semester 80% of MTH 225 students…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

4. Last semester 80% of MTH 225 students were in good standing heading into the final exam (i.e. current grade % was at least 70%). 85% of the students in good standing heading into the final exam scored 65% or better on the final (i.e. passed). Only 10% of students not in good standing scored passed the final exam. (a) What is the probability a randomly selected student passed the final exam? (b) Given that a student passed the final exam, what is the probability the student was in good standing heading into the final exam?

Expert Solution

Step 1

Consider the following events:

$G o o d S \tan d i n g$ : the event that a student is in good standing heading into the final exam.

$P a s s$ : the event that a student pass on the final exam.

$N o t G o o d S \tan d i n g$ : the event that a student is not in good standing heading into the final exam.

For the defined events, it is interpreted that:

The prob. that a student is in good standing heading into the final exam, $P (G o o d S \tan d a i n g) = 80 % = 0.80$ .

The prob. that a student passes the final exam provided that the student is in good standing heading into the final exam, i.e., $P (P a s s | G o o d S \tan d i n g) = 85 % = 0.85$ .

The prob. that a student passes the final exam provided that the student is not in good standing heading into the final exam, i.e., $P (P a s s | N o t G o o d S \tan d i n g) = 10 % = 0.10$ .