Among 500 freshmen pursuing a business degree at a university, 320 are enrolled in an Economics course, 225 are enrolled in a Mathematics course, and 140 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 ... A) an economics and/or a mathematics course?B) exactly one of these two courses?C) neither an economics course nor a mathematics?

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Asked Nov 6, 2019
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Among 500 freshmen pursuing a business degree at a university, 320 are enrolled in an Economics course, 225 are enrolled in a Mathematics course, and 140 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 ... 

A) an economics and/or a mathematics course?

B) exactly one of these two courses?

C) neither an economics course nor a mathematics?

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Expert Answer

Step 1

Probability of an event:

The formula for probability of an event is as follows.

Number of favorable outcomes
P(E)
Total Number outcomes
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Number of favorable outcomes P(E) Total Number outcomes

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Step 2

A.Computing the probability that a freshman selected is enrolled in economics or mathematics course:

The probability that a freshman selected is enrolled in both courses is as follows:

P(Economics and mathemati cs) = P(Both)
140
500
0.28
The required probability is as follows:
P(Economics or mathematics) P(Economics)+P(mathematics)-P(Both)
320 225 140
500 500 500
405
500
0.81
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P(Economics and mathemati cs) = P(Both) 140 500 0.28 The required probability is as follows: P(Economics or mathematics) P(Economics)+P(mathematics)-P(Both) 320 225 140 500 500 500 405 500 0.81

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Step 3

B.Computing the probability that a freshman selected is enrolled in exactly one of th...

P(Exactly one course) = P(Economics only )+ P(mathematics only)
320 140
225-140
500
500
180
85
500
500
265
500
=0.53
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P(Exactly one course) = P(Economics only )+ P(mathematics only) 320 140 225-140 500 500 180 85 500 500 265 500 =0.53

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