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
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To answer these questions, we will need to use some basic probability concepts and the information given in the exercise. Let's go through each question step by step.
16. To find the probability that a randomly selected student will be either a woman or an art major, we need to add the probabilities of these two events occurring. However, we also need to be careful not to double-count the students who are both women and art majors.
The probability of a randomly selected student being a woman is given as 43%. The probability of a randomly selected student being an art major is given as 15%. The probability of a student being both a woman and an art major is given as 8%.
To get the probability of either being a woman or an art major, we can add the individual probabilities and subtract the probability of being both a woman and an art major:
P(woman or art major) = P(woman) + P(art major) - P(woman and art major)
= 43% + 15% - 8%
= 50%
Therefore, the probability that a randomly selected student will be either a woman or an art major is 50%.
17. To find the probability that a randomly selected student is not a woman, we subtract the probability of being a woman from 100% since the probability of an event occurring plus the probability of the event not occurring equals 100%.
P(not a woman) = 100% - P(woman)
= 100% - 43%
= 57%
Therefore, the probability that a randomly selected student is not a woman is 57%.
18. To find the probability that a randomly selected student is either an art major or has not chosen a major, we need to add the probabilities of these two events occurring. In this case, we don't need to worry about double-counting since the two events are mutually exclusive.
The probability of a randomly selected student being an art major is given as 15%. The probability of a randomly selected student not having chosen a major is given as 4%.
To get the probability of either being an art major or not having chosen a major, we can simply add the individual probabilities:
P(art major or not chosen major) = P(art major) + P(not chosen major)
= 15% + 4%
= 19%
Therefore, the probability that a randomly selected student is either an art major or has not chosen a major is 19%.