Freshmen GAME 11/10/11
1. A committee of three must be formed from 5 women and 5
men. What is the probability that the committee will be
exclusive to one gender?
2. A homework assignment calls for students to write 5
sentences using a total of 10 vocabulary words. If each
sentence must use two words and no words can be used more
than once, then how many different ways can a student select
the words?
3. Aida got 8 SUSHINATORs for her birthday, 4 dictator-style and
4 math-style. Although she got 2 identical dictator-style dolls,
the other 2 are unique. And although she got 2 identical mathstyle dolls, the other 2 are unique. In how many
distinguishable ways can she line up these 8 dolls on a shelf if
she wants to alternate dictator-style and math-style dolls? (Do
not complain that you’ve already done this problem because
most of you got it wrong  )
4. There are 5 freshmen, 8 sophomores, and 7 juniors in a chess
club. A group of 6 students will be chosen to compete in a
competition. How many combinations of students are possible
if the group is to consist of (a) exactly 3 freshmen? (b) exactly
3 freshmen and 3 sophomores? (c) an equal number of
freshmen, sophomores, and juniors? (d) all members of the
same class?
5. Janice is threading beads on a string. How many patterns can
she create if she has 5 purple beads, 3 green beads, and 2 blue
beads, assuming she must use all 10 beads and put them in a
circle (left and right do not matter)?
Sophomores GAME 11/10/11
1. A point is chosen at random on a segment that is 24
centimeters long. Find the probability that the chosen
point is at least five times as far from one endpoint as it is
from the other endpoint. Report your answer as a
reduced common fraction.
2. A point is chosen at random inside a circle. Find the
probability that the chosen point is closer to the circle
than it is to the center of the circle. Report your answer as
a reduced common fraction.
3. A point is chosen at random from the interior of an
isosceles right triangle. Find the probability that the
chosen point is closer to the right angle vertex than it is to
the other two vertices. Report your answer as a reduced
common fraction.
4. In a triangle ABC the measure of angle A is and the
measure of angle B is . A ray is chosen at random in the
interior of so that the measure of is . If ray meets side
at P, find the probability that P is closer to A than it is to B
or C. Report your answer as a reduced common fraction.
5. Bart and Homer have identical calculators whose random
number generators produce 8-place decimal values
between 0 and 1. Each person generates two random
numbers and records the sum of his generated values. If
you know that Bart’s sum is 1.40000000, what is the
probability that Homer’s sum will be larger than Bart’s
sum? Report your answer as a decimal rounded to the
nearest hundredth.
Juniors GAME 11/10/11
1. A city survey found that 47% of teenagers have a part time
job. The same survey found that 78% plan to attend
college. If a teenager is chosen at random, what is the
probability that the teenager has a part time job and plans
to attend college?
2. In a school, 14% of students take drama and computer
classes, and 67% take drama class. What is the probability
that a student takes computer class given that the student
takes drama class?
3. In a shipment of 100 televisions, 6 are not defective. If a
person buys two televisions from that shipment, what is
the probability that both are defective?
4. In the United States, 56% of all children get an allowance
and 41% of all children get an allowance and do household
chores. What is the probability that a child does household
chores given that the child gets an allowance?
5. In a basketball tournament, 3 of the participating teams Lion, Panther and Jaguar have the probabilities of 4/15,
3/10 and 1/5 respectively of winning the tournament. Find
the probability that Lion or Jaguar will win the
tournament.
Seniors GAME 11/10/11
1. A large basket of fruit contains 3 oranges, 2 apples
and 5 bananas. If a piece of fruit is chosen at
random, what is the probability of getting an orange
or a banana?
2. In a class of 30 students, there are 17 girls and 13
boys. Five are A students, and three of these
students are girls. If a student is chosen at random,
what is the probability of choosing a girl or an A
student?
3. In the United States, 43% of people wear a seat belt
while driving. If two people are chosen at random,
what is the probability that both of them wear a seat
belt?
4. In a school, 18% of students take drama and
computer classes, and 64% take drama class. What is
the probability that a student takes computer class
given that the student takes drama class?
5. In a shipment of 100 televisions, 6 are defective. If a
person buys two televisions from that shipment,
what is the probability that both are defective?