Nursing majors Nonnursing majors Total Males 96 1108 Females

Nursing majors

Non-nursing majors

Total

Males

96

1108

Females

600

1724

2324

Total

696

2736

3432

The table above shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through (d).

(a) Find the probability that the student is male or a nursing major.

(b) Find the probability that the student is female or not a nursing major

(c) Find the probability that the student is not female or a nursing major.

(d) Are the events \"being male\" and \"being a nursing major\" mutually exclusive? explain

Solution

(a) Find the probability that the student is male or a nursing major.

P(male or a nursing major) = P(male) + P(nursing major) - P(both)

=1108/3432 + 696/3432 - 96/3432

=0.497669

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(b) Find the probability that the student is female or not a nursing major

P(female or not a nursing major) = P(female) + P(not a nursing major) - P(both)

=2324/3432 + 2736/3432 - 1724/3432

=0.972028

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(c) Find the probability that the student is not female or a nursing major.

P(not female or a nursing major) = P(not female) + P(a nursing major) - P(both)

=0.497669

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(d) Are the events \"being male\" and \"being a nursing major\" mutually exclusive? explain

No, because P(being male and being a nursing major) is not equal to 0