Multiple
Choice Items:
Use the following information to answer
questions 1–3.
Isaac works in an auto parts store and he
keeps track of the inventory. He works hard but doesn’t always save
his files on the right server. The probability he finds File A on the
first try is 0.40. The probability he finds File B on the first try
is 0.20. P(C) = 0.20; P(D) = 0.15; and the P(F) = 0.05.

1. What is the probability that Isaac finds file C on the
first try and File A on the first try?


2. What is the probability that Isaac finds File D on the
first try or finds File F on the first try?

A

.20

B

.0075

C

.1925

D

.10


3. What is the probability that Isaac finds File A on the
first try, given he found File D on the first try?

Use the following information to answer
questions 4–6.
A family has three children.

4. How many possible outcomes are there for the gender of
three children?


5. What is the probability that of the three children, at
least two of them are boys?


6. What is the probability the family’s third child is a
girl, given their first child was a boy?


7. If the probability of winning a random drawing is , what
are the odds against winning?

A

1:2000

B

2000:1

C

1:1999

D

1999:1


8. In a standard 52card deck, the odds of drawing a face
card are 3:10; what is the probability of drawing a facecard?

 A

 3/10

B

3/52

C

3/13

D

3/26


9. When Jason flips a fair coin, there is an equal
probability of headsup or tailsup. Jason flipped the coin 3 times.
It landed headsup all 3 times. What is the probability the coin
will land headsup the next time Jason flips the coin?

Multiple
choice key:
1. B

2. A

3. A

4. D

5. A

6. B

7. D

8. C

9. A


Short
Answer Items:

10. Make a tree diagram/list of all
possible gender outcomes of two sets of twins.

11. Suppose that in a certain high
school class, 50% of the students have brown eyes, 30% have blue
eyes, 12% have green eyes, and 8% have hazel eyes. What is the
probability that two students chosen at random have the same eye
color?

12. Consider the nine multiplechoice
questions at the beginning of the test.

a) What is the probability of
answering one correctly by randomly guessing?

b) What is the probability of
answering them all correctly by guessing?

13. The table shows some population
percentages for the United States based on the year 2000 census.
U.S. Population
Percentages according to age in 2000

Gender

Under 18

18 and older

Male

26.8

73.2

Female

24.6

75.4


A random U.S. adult (age 18 and older) is selected; find the
probability that the adult is male.

b) A random U.S. female is selected; find the probability
that she is under 18.
Shortanswer
key and Scoring Rubric:

10. Answer: Tree/sample space
should show the following outcomes: (16)

MMMM, FMMM, MFMM, MMFM, MMMF,
FFFF, MFFF, FMFF, FFMF, FFFM, MMFF, FFMM, FMFM, MFFM, FMMF, MFMF

11. Answer: (.5 × .5) + (.3 × .3)
+ (.12 × .12) + (.08 × .08) = .3608

12. Answer: a) 1/4 b) (1/4) ^{9}
= .000003815

13. Answer: a) .50 × .732 =
.366 or 36.6%

b) .50 × .246 = .123 or 12.3%
Points

Description

2


Response is complete, correct, and detailed.

Student demonstrates thorough understanding of compound
probabilities.
 Supporting work is complete and correct.

1


0


Performance
Assessment:
The game 500 is played with six standard
sixsided number cubes and two or more players. The basic rules for
this game can be found at http://en.wikipedia.org/wiki/Farkle.
500 is a variant of Farkle in which each player must continue rolling
the remaining number cubes on his/her turn until reaching an initial
threshold of at least 500 points. After the threshold is reached, the
player may stop at any time and may play freely (with no further
threshold) on subsequent turns. Players who “farkle” on their
first turn, prior to reaching the threshold, must continue to strive
for that threshold on subsequent turns. 500 is played to a winning
score of 500 points.
Farkle is played by two or
more players, with each player in succession having a turn at
throwing the number cubes. Each player’s turn results in a score,
and the scores for each player accumulate to some winning total.
At the beginning of each turn, the
player throws all six 6sided number cubes.
After each throw, one or
more scoring number cubes must be set aside.
1s and 5s are always scorable; 2s, 3s, 4s, and 6s are only scorable
when they occur in a set of three or more
(e.g., 2, 2, 2).
The player may then either
end his/her turn and bank the score
accumulated so far, or continue to throw the remaining number cubes.
If the player has scored all six number cubes, s/he has “hot cubes”
and may continue his/her turn with a new throw of all six number
cubes, adding to the score already accumulated.
If no
number cubes score in any given throw, the player has “farkled”
and all points for that turn are lost.
At the end of the player’s
turn, the number cubes are handed to the next player in succession
(usually in clockwise rotation), and that person takes a turn. Once a
player has achieved a winning point total, every other player has one
last turn to score enough points to surpass that high score.
Here is an example of play:

Player 1

First roll: 1, 2, 4, 4, 6, 6 Sets
aside: 1 (100 points)

Second roll: 3, 5, 5, 6, 6 Sets
aside: 5 (50 points)

Third roll: 1, 1, 2, 5 Sets aside: 1,
1 (200 points)

Fourth roll: 3, 4 (farkle)
Since only 350 total points have been
accumulated, Player 1 has not met the initial 500point threshold,
and scores 0. Player 1 must attempt to reach this threshold again on
his/her next turn.

Player 2

First roll: 2, 3, 3, 3, 5, 6 Sets
aside: 3, 3, 3 (300 points)

Second roll: 1, 4, 5 Sets aside: 1, 5
(150 points)

Third roll: 1 Sets aside: 1 (100
points)
Since 550 total points have been
accumulated, Player 2 now has the option to stop (recording a score
of 550 for the first turn), or reroll all six “hot cubes” and
attempt to add to the first turn’s score. If, however, Player 2
should farkle after rerolling, all scoring would be lost and the
threshold would be, in effect, on Player 2’s next turn.
Performance Task:
Determine whether there is a winning
strategy when playing 500.
Your analysis of the game should include:

experimental data collected from playing 500 using various
strategies;

varying analysis for different game situations, such as
aiming for the 500point threshold, how many scoring number cubes to
set aside, whether to set aside or break up triples, how to play
when nearing 5,000 points, etc.;

identifying various types of events that could happen in the
game, classifying each as dependent or independent; and

the calculation of theoretical probabilities, using the
concepts learned in the Compound Probability unit.
(Recommendation to the teacher: On the day
the Performance Task is due, set up a 500 tournament in which
students are forced to use their winning strategy!)
Score

Experimental Data

Analysis

Event Identification

Theoretical Calculation


20%

50%

10%

20%

4

Must indicate that a sufficient number
of turns have been taken to get passed rolling a losing number.
More than sufficient data has been collected in order to observe
patterns and draw conclusions.
Four or more strategies are exhaustively
tested.

Analysis covers almost every conceivable
game situation, even beyond those given as examples.
The probabilitybased justifications are
without error.
The analysis is good enough to be part
of a published strategy guide for the game.

List of events is exhaustive.
Sequences of events are properly
identified as being dependent or independent.

Theoretical probability calculations are
correct and relevant.
The entire base of learning from the
unit is displayed, including advanced topics like expected value
and combinations.

3

Sufficient data has been collected in
order to observe patterns and draw conclusions.
At least three different strategies are
part of the experiment.

Analysis covers at least the game
situations mentioned in the examples in the Performance Task
description.
It uses the experimental data and
theoretical probabilities as strong supporting justification.
The existence/nonexistence of winning
strategies is clear.

A thorough list of related simple events
has been created.
Sequences of events are properly
identified as being dependent or independent.

Theoretical probability calculations are
correct and relevant.
They demonstrate the addition and
multiplication rules of probability, using tools like probability
trees and definitionbased formulas.

Performance
Assessment Scoring Rubric:
2

The experiment includes only two
strategies, or sample size is insufficient to draw
conclusions for at least one of the strategies.

At least one of the example game
situations is not analyzed.
Analysis may be a bit shaky, with
incomplete justification, but the conclusion about the existence
of winning strategies is still clear.

List of events is missing a few key
events.
One or two events may be misidentified.

Theoretical probability calculations may
show small errors.
Major topics from the unit are
identifiable in the student’s work.

1

Conclusions are weak and unsubstantiated,
or only one strategy is tested.

Multiple examplegame situations are not
analyzed; analysis may simply be general in nature.
Analysis is shoddy, trivial, or largely
incorrect.
Conclusion may be unclear.

Many obvious events are missing from the
list, or misidentification of events is extensive and makes
it clear that the student does not understand event dependence.

Theoretical probability calculations are
largely incorrect or irrelevant to the Performance Task.
Major topics from the unit may be missing
entirely.

0

Experimental data is not included.

Performance Task is never completed.

List of events is not included.

Theoretical probabilities are not present
or are entirely irrelevant to the Performance Task.
