Download Math 10 Name KcU Exam 4: Chapter 12 3 " 1. Match the word with

Math 10
Exam 4: Chapter 12
Name
KcU
3"
Each problem is worth 10 points. You must show all work to receive full credit.
1. Match the word with the definition.
Deflnitions
i.
An
ii.
iii.
\
Words
is a controlled operation that yields a set of results.
a.
event
The possible resuhs of an experiment are called its \
b.
sample point
An
c.
permutation
d.
mutually
i^'^ is a subcoUection of the outcomes of an experiment.
iv.
is the relative frequency of occurrence of an event and is
detei mined by actual observations of an experiment.
I
V.
exclusive
is detei mined through a study of the possible outcomes that can
e.
occur for the given experiment.
vi.
probability
If each outcome of an experiment has the same chance of occurring as
f
any other outcome, they are said to be \
vii.
A list of all possible outcomes of an experiment is called a
viii.
ix.
\
( \f it is impossible for both events to occur
g-
combination
h.
tree diagrams
i.
theoretical
simultaneously.
X.
Event A and event B are
independent
events
V \e illustrated flow charts used to determine sample spaces.
Two events A and B are
conditional
probability
^
if the occurrence of either event in no
J-
sample space
k.
equally likely
way affects the probability of occurrence of the other event.
xi.
The probability of event Ej occurring, given that an event E\s
happened (or will happen; the time relationship does not matter), is
outcomes
called a \d is written P(ii2|£'i).
xii.
A
xiii.
A
(
is any ordered arrangement of a given set of objects.
' ^ is a distinct group (or set) of objects without regard to their
1.
experiment
m.
empirical
arrangement.
probability
n.
2, If P(A)=0,1, P(B)=0.4, and P(A or B)=035, thenfindP(A and B).
outcomes
Two fair dice are rolled. Find the probability of each of the following:
a. P(the sum of the two numbers is 5).
)(2^JK<4)(2,5)(2,6)
,2) (^3) (3,4) (3,5) (3,6)
b. P(the sum of the two numbers is even).
1>(4,2) (4,3) (4,4) (4,5) (4,6|^
((5,;) (5,2) (5,3) (5,4) (5,5) (5^j
c. P(the sum of the two numbers is less than 5).
(6,1) (6^) (6,3) (6,4) (6,5)
d. P(the sum of the two numbers is even A N D less than 5). -
e. P(the sum ofthe two numbers is even OR less than 5).
(6^j)
^(jl'^/tN^
'
^
5C
d<b
ONE card is drawn at random from a standard 52-card deck. Find the probability of each of the
following:
a. P(the card is a king). — M _ \
5l'
b. P(the card is not a king). _
J
c. P(the card is a number less than 5).
d. P(the card is a number less than 5 OR *).
57.
52-
e. P(the card is greater than 3 and less than 6 A N D *).
A fair coin is tossed 3 times. The sample space is hsted below,
a. Find P(coin landing on exactly two heads). A
Sample Space
b. Find P(coin landing on no heads).
II
HHH
HHT
c. Find P(coin landing on at least one heads)\
HTH
HTT
THH
d. Find P(coin landing on exactly two heads / T' was heads).
THT
TTH
e. Find P(coin landing on no heads /1^' was tails).
TTT
6. A restaurant's lunch specials include soup or salad, chicken or fish, and water or tea or soda,
a. How many ways can you have lunch?
appetizer
meal
beverage
total numberof ways
b. Draw a tree diagram and list the sample space.
Sample Space
c. Find P(having fish / that you had a salad).
3 ^rn
d. Find P(having soup and tea).
e. Find P(not having chicken nor soda).
1
3
7. Two marbles are drawn from a box with 3 white, 2 green, 2 red, and 1 blue marble.
a. Find P(both marbles are white), if the marbles were drawn one at a time with replacement.
b. Find P(both marbles are white), if the marbles were drawn one at a time without replacement.
&
^ ^ ^ ^
c. Find P(one marble is white and one marble is blue), if the marbles were drawn one at a time with
replacement.
16 fc
d. Find P ( l ' ' marble is white and 2""^ marble is blue), if the marbles were drawn one at a time without
replacement.
e. Say the marbles were drawn at the same time. Find P(one marble is white and one marble is blue,
regardless of order), if the marbles were drawn at the same time without replacement.
8. A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at
random.
a. Find P(all 3 candies are cherry), if the candies were drawn at the same time without replacement.
b. Find P(no cherry candies), i f the candies were drawn at the same time without replacement.
c. Find P(at least 1 cherry candy), i f the candies were drawn at the same time without replacement.
' Pipe cbm)
3 5 ' \'o
d. Find P(exactly 2 cherry candies and any other candy, in any order), if the candies were drawn at the
same time without replacement. ,
\: |
e. Say the candies were drawn one at a time. Find P(r' is cherry, 2"*^ is orange, and 3''^ is lemon), i f
they were drawn without replacement.
9. A license plate is to consist of 2 letters followed by 3 digits. Determine the number of different license
plates possible i f
a. Repetition of letters and number^s permitted.
L
L
#
«
#
N
^
b. Repetition of letters and numbers is NOT permitted.
L
L
#
#
#
c. The r' letter has to be a vowel (a, e, i, o, u) and the l " number has to be less than 4. Also, repetition
of letters and numbers is permitted.
L
L
#
#
ft
d. The 1^' letter has to be a vowel (a, e, i, o, u) and the 1^' number has to be less than 4. Also, repetition
of letters and numbers is NOT permitted.
L
L
U
#
U
'
10. Calculate
11. Calculate
a. X „
12. You want to arrange 5 books (math, science, history, biology, and English) on a bookshelf
a. How many different ways can all 5 books be arranged?
b. How many different ways can the 5 books be arranged i f math is in the middle?
iL 1 .1. ^ -L =|l4_\
c. How many different ways can the 5 books be arranged if math is in the middle and history is on the
end?
V
:^ ^ A_ 1-
=\(^
d. How many different ways can the 5 books be arranged i f science is first, math is in the middle and
history is on the end?
e. How many different ways can the books be arranged if you threw out 2 books and only kept 3 of the
13. How many ways can you arrange the word COMMUNICATION?
14. Say there were 7 women and 5 men applying for 7 positions at a company.
a. Find the number of different combinations the company can hire the 7 people.
b. Find the number of different combinations the company can hire the 7 people, if 4 have to women
and 3 have to be men.
15. A pool table has balls numbered 1-15, where 7 are striped and 8 are solid. You randomly shot in 5 balls
all at the same time. Use combinations to calculate the following:
a. P(you shot in all 5 solids).
^
\
b. P(you shot in all 5 stripes).
c. P(you shot in all 5 balls numbered greater than^).
d. P(you shot in 3 stripes and 2 solids at the same time).
e. P(you shot in 3 stripes, and then 2 solids).