Download 11/3 Probability Review Packet

FST 11/3/16
Probability and Counting Review
Name: ____
1.
What is the difference between a permutation and a combination?
2.
Complete the table of CHS students’ favorite extra-curricular. Use the chart to determine each
probability.
a.
P(junior)
Sports Performing
Arts
Sophomore
140
50
Junior
150
Total
50
Total
3.
4.
Write a problem for each situation.
P
a.
20 3
P(performing arts)
c.
P(sophomore or performing arts)
d.
P(junior and sports)
e.
P(junior|sports)
b.
C 11
72
Given two solutions to “How many Internet codes can be made by using 3 digits if 0 is
excluded and digits may not be repeated?”, who is correct? Explain.
Student A
9!
3!(9-3)!
5.
b.
Student B
9!
(9 − 3)!
How many ways can a jury of 12 and 2 alternate jurors be selected from 30 potential jurors?
6.
A paper clip holder has 100 paper clips: 30 are red, 25 are yellow, 15 are pink, 11 are blue, and
19 are green.
a.
A paper clip is randomly chosen. What is the probability that the paper clip is yellow?
b.
A paper clip is randomly chosen. What is the probability that the paper clip is NOT
green?
c.
Two paper clips are chosen WITH replacement. What is the probability that the first
paper clip is red and the second paper clip is pink?
d.
Two paper clips are chosen one at a time WITHOUT replacement. What is the
probability that both paper clips are green?
e.
Three paper clips are chosen one at a time WITHOUT replacement. What is the
probability that you choose 1 red, then 1 yellow, and finally 1 green?
f.
Two paper clips are chosen one at a time WITHOUT replacement. Find P(1 blue AND
1 red).
g.
Two paper clips are chosen one at a time WITH replacement. Find P(2 blue OR 2 red).
7.
State Farm Insurance Company received ten claims for car accidents during one week.
Management decides to select three of these claims randomly and to investigate them
thoroughly. In how many different ways can this be done?
8.
Each of the 8 questions on a multiple-choice test has 5 possible answers. If all the questions are
answered, in how many ways can the test be completed?
9.
Katie’s art store makes custom paints using a base, a texture, and a pigment. If the store has 3
different bases, 2 textures, and 18 pigments, how many different custom paints can be mixed?
10.
There are 10 pennies, 8 nickels, and 5 dimes in a bank.
11.
a.
You are selecting 4 coins with replacement. Find P(all pennies).
b.
You are selecting 4 coins with replacement. Find P(all quarters).
One card is chosen at random from a standard deck. Calculate the following probabilities.
a.
P(8 or a Heart)
b.
P(Queen or a King)
c.
P(Ace or a Red Card)
12.
13.
Two cards are chosen at random from a standard deck. Calculate the following probabilities.
a.
P(King then a Heart) WITH replacement.
b.
P(King then a King) WITH replacement.
c.
P(King then a King) WITHOUT replacement.
Student Government consists of 28 members, 16 males and 12 females.
a.
Four members are chosen to be directors. How many different 4-person groups of
directors are possible?
b.
If the group of directors must be two males and two females, how many different 4person groups of directors are possible?
c.
Suppose that STUGO decides to elect ranked officers. If a President, Vice-President,
Secretary, and a Treasurer are chosen as officers, how many different outcomes are
possible?
d.
Suppose that STUGO decides to select only a President and Vice-President and they
must be of different genders. How many different outcomes are possible?
14.
The members of the math club plan to create a secret language using the symbols below. They
will create “words” by arranging the following symbols:
, ≅ , ∞, ∪ , Σ, Δ,
15.
16.
∫
, ⊥, θ
a.
If each symbol can be used more than once, how many 5 “letter words” can be formed?
b.
If each symbol cannot be used more than once, how many 5 “letter words” can be
formed?
Given a standard deck of cards.
a.
How many different 5-card hands are possible?
b.
In how many 5-card hands are all 5 cards diamonds?
c.
What is the probability of getting 5 diamonds in a 5-card hand?
Mr. Kohmetscher was watching a special program on ancient artifacts. One of his favorite
artifacts was a gold medallion with 9 unique symbols. How many ways can the symbols be
arranged on the medallion?
*
!
#
<
@
&
!
$
%
17.
Next year you are going to take one science class, one math class, one history class, and one
English class. According to the schedule you have 5 different science classes, 3 different math
classes, 3 different history classes, and 4 different English classes to choose from. Assuming no
scheduling conflicts, how many different four-course selections can you make?
18.
Consider the experiment in which you record the outcome of rolling one six-sided die numbered
1-6 and a fair four-sectioned spinner numbered 1-4.
19.
a.
Give the experiment’s sample space.
b.
In your sample space from part a, circle the outcomes in the event “the spinner shows
an even number”
c.
What is the probability of the event “the spinner shows an even number or the die is
even”?
While writing a test, Mr. Rust discovered that there are only a couple of 15-letter words that
do not repeat a letter. One of the words is DERMATOGLYPHICS.
a.
How many unique “words” can be formed using all 15 letters?
b.
How many of these arrangements start with DER?
c.
If the one restriction is that the M and the A must stay together, how many
arrangements are possible?
d.
How many groups of 4 letters can be selected from this 15-letter word?
20.
Given P(A) = .42, P(B)= .37, and P(A ∪ B) = .6346.
a.
Find P(A ∩ B).
b.
Based on the given information and what you found in part a, why do we know that A
and B are not mutually exclusive?
c.
What assumption did you make to determine your answer to part a?
d.
Fill in the 4 blanks in the Venn Diagram.
B
e.
Find P(Not A)
A
21.
The table below shows the probability distribution of the number of bases for a randomly
selected time at bat for a member of the St. Louis Cardinals. In other words, 71.8% of the atbats the player was out, 17.4% of the time the player got a “single”, etc.
St. Louis Cardinals Hitting
# of Bases
Probability
0
0.718
1
0.174
2
0.065
3
0.004
4
0.039
22.
a.
Find the expected value for the number of bases for an at bat.
b.
In the context of the problem, explain the meaning of the expected value.
An urn contains 8 white, 6 blue, and 9 red balls. How many ways can 6 balls be selected to
meet each condition?
a.
All the balls are red.
b.
Three are blue, 2 are white, and 1 is red.
c.
Two are blue, and 4 are red.
d.
Exactly 4 balls are white.