Among 500 freshmen pursuing a business degree at a university, 349 are enrolled in an economics course, 235 are enrolled in a mathematics course, and 136 are enrolled in both an economics and a mathematics course. What is the probability that a freshman selected at random from this group is enrolled in each of the following? (Enter your answers to three decimal places.) (a) an economics and/or a mathematics course (b) exactly one of these two courses (c) neither an economics course nor a mathematics course

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ISBN:9780470458365
Author:Erwin Kreyszig
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Among 500 freshmen pursuing a business degree at a university, 349 are enrolled in an economics course, 235 are enrolled in a mathematics course, and 136 are enrolled in both an economics and a mathematics course. What is the probability that a freshman selected at random from this group is enrolled in each of the following? (Enter your answers to three decimal places.)

(a) an economics and/or a mathematics course


(b) exactly one of these two courses


(c) neither an economics course nor a mathematics course
Expert Solution
Step 1

Sol:-

We can use a Venn diagram to solve this problem. Let E be the event that a student is enrolled in an economics course, and let M be the event that a student is enrolled in a mathematics course. Then we have:

Number of students enrolled in E = 349

Number of students enrolled in M = 235

Number of students enrolled in both E and M = 136

 

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