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1) Figure 2.2 shows the counts of earned degrees for several colleges on the East Coast. The level of degree and the gender of the degree recipient were tracked. Row & Column totals are included.
[Figure8]
a) What is the probability that a randomly selected degree recipient is a female?
b) What is the probability that a randomly chosen degree recipient is a man?
c) What is the probability that a randomly selected degree recipient is a woman, given that they received a Master's Degree?
d) For a randomly selected degree recipient, what is P(Bachelor's Degree|Male)?
2) In poker, 5 cards are dealt to a player. One of the stronger poker hands is a flush. This means that all 5 cards are of the same suit, for example, all hearts. What is the probability of being dealt a flush?
3) The table below shows the probability breakdown of ages and genders for the typical American college student. Each value in the table is given as a probability. For example, there is a 12% chance that a randomly selected college student will be a male between 25 and 34 years old.
a) What is the probability that a randomly selected American college student is female?
b) What is the probability that a randomly selected American college student is female given that the student is more than 34 years old?
c) What is the probability that a randomly selected college student is either a female or more than 34 years old?
4) Suppose that 40% of adults like eating bananas while 60% like eating apples. Suppose also that 32% of adults like eating both. What is the conditional probability that a randomly selected adult likes apples given that they like bananas? Use a Venn Diagram to answer this question.
5) Another good poker hand is called a straight. This means that your five cards will be numerically in order such as an 8, 9, 10, jack, and queen. The cards do not need to match suit in a straight. Suppose you receive the first four cards of a five card poker hand. You have 5♥, 7♦, 8♣, and 9♦. What is the probability that the next card will give you a straight?
[Figure9]
6) Suppose you receive the first four cards of a five card poker hand. You have 3♥, 4♦, 5♣, and 6♦. What is the probability that your next card will give you a straight?
7) A statistics class has 18 juniors and 10 seniors in it. 6 of the seniors are females and 12 of the juniors are males. Build a contingency table to find the probability that a randomly selected student is:
a) a junior or a female?
b) a senior or a female?
c) a junior or a senior?
d) a female given that the student was a senior?
8) At a used-book sale, there are 120 children’s books and 80 adult books available. 50 of the adult books are nonfiction while 40 of the children’s books are nonfiction. All other books are fiction. Build a contingency table to find the probability that a randomly selected book is:
a) fiction.
b) not a children’s nonfiction
c) an adult book or children’s nonfiction.
d) a children's book given that it was nonfiction.
9) Animals on the endangered species list are given in the table below by type of animal and whether it is domestic or foreign to the United States.
An endangered animal is selected at random. What is the probability that it is:
a) a bird found in the United States?
b) foreign or a mammal?
c) a bird given that it is found in the United States?
d) a bird given that it is foreign?
[Figure10]
10) Suppose a standard set of pool balls (1-8 are solid and 9-15 are striped) are in a bag. Two balls are picked out of the bag without replacement.
a) Find the probability that second ball is odd given that the first ball was the 10 ball.
b) Find P(2nd striped|1st solid).
11) Cable channels 6, 8, & 10 show quiz shows, comedies, & dramas. The table below shows the distributions of these shows.
If a show is selected at random, find the probability that the show is:
a) a quiz show or shown on Channel 8.
b) a drama or a comedy.
c) a comedy given that it is shown on Channel 8.
d) shown on Channel 6 given that it is a drama.
12) Suppose you receive your first three cards of a five card poker hand. You have 5♦, 6♦, 7♥. What is the probability that your next two cards will result with you having a straight?
Review Exercises
13) Suppose that 25% of all 9th graders have an unweighted GPA after their 9th grade year of 3.5 or higher. Also suppose that 60% of all 9th graders are involved in a sport at some time during their 9th grade year. Assume that a student's GPA and whether or not they are in a sport are independent of one another. Draw and label a tree diagram for this situation and build a probability model that summarizes the different probabilities possible for 9th grade students in regards to GPA and a sport.
14) A special deck of cards contains only the face cards and aces from a standard deck of cards.
a) If one card is dealt, what is the probability that the card is an ace?
b) If one card is dealt, what is the probability that the card is a black ace?
c) If two cards are dealt, what is the probability that both cards are face cards?
15) Suppose for a moment that all months have exactly 30 days and the chance of you being born in any particular month is . What is the probability that neither of two randomly selected people will have been born in the same month as you?
16) The standard California license plates made in 2011 or later must begin with a digit from 6 to 9 followed by a letter anywhere from T to Z. They then have any two letters followed by any three digits. How many of these license plates are possible?
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