Wilmington University Compute the Probability Mathematics Questions

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1. The Venn diagram below shows the 12 students in Mrs. Chang’s class. The
diagram shows the memberships for the Orchestra and the Chess club.
Orchestra
Chess
Jill
Ana
Mia
John
Pedro
Giosue
Quinn
Lisa
Tom
Ben
Kathryn
Lian
Note that “Lian” is outside the circles since she is not a member of the Orchestra or the
Chess Club. One student from the class is randomly selected.
Let A denote the event “the student is in the Orchestra”.
Let B denote the event “the student is in the Chess Club”.
Find the probabilities of the events below
P(A) =
P(B) =
P(A or B) =
P(A and B)
=
P(A) + P(B) – P(A and B)
2. Maria is planning day trips over the next year. She plans to visit 3 historical
museums, 5 art museums, 4 art galleries, and 7 amusement parks. What is the
probability that her first trip takes her to a place where art is shown or that is a
museum?
3. A pet store has 15 puppies: 5 Beagles, 6 Collies, and 4 Dobermans. Two
customers purchase puppies. Find the probability that the first customer buys a
Collie and the second customer buys a Beagle.
4. It is estimated that 60% of fifth graders have gone camping, and that 23% have
gone camping and seen a bear. A total of 35% have seen a bear. Round your
answers to the nearest hundredth.
a. What is the probability that a randomly selected fifth grader has seen a bear,
given that he or she has been camping?
b. What is the probability that a randomly selected fifth grader has been camping,
given that he or she has seen a bear?’
5. An urn contains 5 blue and 5 red balls. Four balls are randomly drawn from the
urn in succession, with replacement. That is, after each draw, the selected ball
is returned to the urn. What is the probability that all 4 balls drawn from the um
are red? Round your answer to 3 decimal places.
Extra Credit
1. A spinner has 8 equally sized slices numbered from 1 to 8. Answer each
question as a fraction. The wheel will be spun and will stop on a slice at
random. (1 and 8 are purple, 2 and 3 are yellow, 4, 5, and 6 are blue, and 7 is
red)
a. What is the probability that the wheel stops on the number 4?
b. What is the probability that the wheel stops on number 4, given that the wheel
stops on blue?
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