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Larson Geometry

PT: Sample Space & Size, Independent Events

RW: Die

Consider rolling polyhedron dice.  Each die are numbered on each face, beginning with one.

What is the probability of:

a)      Rolling a 3 on an octagon die?

b)      Rolling a 3 on an iscosahedron die?

c)      Rolling a 3 on a tetrahedron die?

d)      Rolling a 2-digit number on a dodecahedron die?

e)      Rolling a pair of 8’s on a dodecahedron and octagon dice?

Larson Geometry

PT: Sample Space & Size, Simple Event

RW: Hot Air Balloons

In a "Hare and Hounds" balloon race, one balloon (the hare) leaves the ground first.  About 10 minutes later, the other balloons (the hounds) leave.  The hare then lands and marks a square region as the target.  The hounds each try to drop a marker in the target.

a)   Suppose that the hounds’ markers are equally likely to land anywhere in a rectangular field that is 200 feet by 250 feet.  The target is a 20X20 square that lies in the field.  What is the probability that the marker lands in the target?

b)    If the area of the target is doubled, how does the probability change?

c)   If each side of the target area is doubled, how does the probability change

Glencoe Algebra 1

PT: Sample Space

Draw two plane figures that have equal probability of choosing a point at random where one of the figures looks less probable then the other.

Glencoe Algebra 1, p. 413

PT: Permutations, Sample Space

RW: Archaeology

A group of college archaeology students are traveling to the Virgin Islands to study Carib Indian relics and the remnants of the forts built by the Danes.  The Carib Indians were the original occupants of the islands but had died or left by early 1600s. The Danes formally claimed the islands in 1666 and controlled them until 1917.  The group’s advisor must decide how the group will get to the Islands.  From their college, they will travel first to Miami, Florida, by car, bus, or plane.  From Miami they can reach St. Thomas in the Virgin Islands by plane or ship.  Suppose the advisor picks the mode of transportation at random.  List all possible modes of transportation to the islands.  Find the probability that they will travel by car first and then fly.

Brown Pre-calculus, p. 603

PT: Sample Size

RW: New York phone numbers

New York City is divided into five boroughs: Manhattan, Queens, the Bronx, Brooklyn, and Staten Island.  Suppose that a New York City telephone number is randomly chosen.

a)  Explain why the probability that it is a Manhattan telephone number is not 1/5.

b)   What do you need to know in order to find the correct probability in part a)?

Brown Pre-calculus, p. 602

PT: Sample space

RW: Coin tossing

A penny, a nickel, and a dime are tossed.

a)   Does the set S = {0, 1, 2, 3}, which gives the four different numbers of "heads" that could come up satisfy the definition of sample space?

b)     What is wrong with reasoning that since one of the four sample points in part a) corresponds to 2 "heads", then P (2 "heads") = ¼?

c)      Draw a tree diagram for this situation.

Brown Precalc, p. 602

PT: Sample space

RW: Card deck

A card is picked at random from a standard deck.  Explain why the set S = {club, spade, red card, face card} is not a sample space.

Brown Pre-calculus, p. 634

PT: Expected Value, Sample Space

RW: Test Taking

On a multiple-choice test, a student is given five possible answers for each question.  The student receives 1 point for a correct answer and loses ¼ point for an incorrect answer.  If the student has no idea of the correct answer for a particular question and merely guesses, what is the student’s expected gain or loss on the question?

Suppose also that on one of the questions you can eliminate two of the five answers as being wrong.  If you guess at one of the remaining three answers, what is your expected gain or loss on the question?

Merrill Algebra 1, p. 606

M: Availability

PT: Sample Space

RW: Baseball championships

There are 208 baseball teams in the state playoff.  If a team loses, it is eliminated and plays no more games.  How many games will be needed to decide the state champion?

Key to Problem Bank: