Math

In Exercises 16–18, use the following information. At a college, 43% of the students are women, 15% of the students are art majors, 4% have not chosen a major, and 8% are women and art majors. A faculty member conducts an experiment and selects students at random to participate.

16. What is the probability that a randomly selected student will be either a woman or an art major?
17. What is the probability that a randomly selected student is not a woman?
18. What is the probability that a randomly selected student is either an art
major or has not chosen a major?


asked by Kms
  1. This can be solved by sketching a Venn diagram.

    Given:
    a. 43% women
    b. 8% women art majors
    c. 15% art major
    d. 4% not chosen major

    16.
    From (a) and (b),
    15-8=7% are male art majors
    So
    P(art major∪woman)
    =43%+7%=50%

    17.
    Assuming all students are either man or woman,
    P(male)=100-43=57%

    18.
    Art major and those who have not chosen are mutually exclusive, so we add probabilities
    P(art major ∪ not chosen)
    =15+4
    19%

    posted by MathMate

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