Applications of Probability Assignment, algebra homework help

Please complete the following questions. It is important that you show all work you did to solve the problems. This includes any calculations, diagrams, or graphs that helped you solve it.

1) Open Ended. Describe a situation in which the number of outcomes is given by P(6, 3).

2) Open Ended. Describe an event that has a probability of 0 and an event that has a probability of 1.

3) Writing in Math. Use the information on page 684 to explain how you can count the maximum number of license plates a state can issue. Explain how to use the Fundamental Counting Principle to find the number of different license plates in a state such as Oklahoma, which has 3 letters followed by 3 numbers. Also explain how a state can increase the number of possible plates without increasing the length of the plate number.Page 684 is in the attachments.

4) Writing in Math. Use the information on page 710 to explain how permutations and combinations apply to softball. Explain how to find the number of 9-person lineups that are possible and how many ways there are to choose 9 players if 16 players show up for a game.Page 710 is in the attachments.

an Ideas
e problem
Mindependent
e pmbles
ing dependent
The number of possible license
plates for a state is too great to
count by listing all of the
possibilities. It is much more
efficient to count the number of
possibilities by using the
Fundamental Counting Principle.
XXH ABE
ORO
Vocabulary
ne
ndent events
mental Counting
Independent Events An outcome is the result of a single trial. For
example, the trial of flipping a coin once has two outcomes: head or tail.
The set of all possible outcomes is called the sample space. An event
consists of one or more outcomes of a trial. The choices of letters and
digits to be put on a license plate are called independent events because
each letter or digit chosen does not affect the choices for the others.
par
Hent events
EXAMPLE Independent Events
O FOOD A sandwich cart offers customers a choice of hamburger,
chicken, or fish on either a plain or a sesame seed bun. How many
different combinations of meat and a bun are possible?
First, note that the choice of the type of meat does not affect the choice
of the type of bun, so these events are independent.
Method i Tree Diagram
II represents hamburger, C, chicken, F, fish, P. plain, and S, sesame sud.
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QUI
Meat
F
ne Math
he both makine
Еe same
space
imple spaceshave
ebbe number of
Bun
—
0 -Y
HP
HS
CP
Possible Combinations
Method 2 Make a Table
ва
3.die. Infmute
follow
he problems
Bohing
mutations
The problems
olving
mbinations
the manager of a softball team fills
out her team’s lineup card before the game,
the order in which she fills in the names is
important because it determines the order
in which the players will bat.
Suppose she has 7 possible players in mind
for the top 4 spots in the lineup. You know
from the Fundamental Counting Principle
that there are 7.6.5.4 or 840 ways that
she could assign players to the top 4 spots.
Vocabulary
permutation
nation
Permutations When a group of objects or people are arranged in a
certain order, the arrangement is called a permutation. In a permutation,
the order of the objects is very important. The arrangement of objects or
people in a line is called a linear permutation.
Notice that 7.6.5.4 is the product of the first 4 factors of 7!. You can
rewrite this product in terms of 7!.
HC
7.6. 5.4 = 7.6.5.4.
3.2.1
Multiply by 1-2.1
ori
or
7. 4. 5.1.3.2.1
or?
7! = 7.6.5.4.3.2.1 and 31 = 3.2.1
M Notice that 3! is the same as 17
The number of ways to arrange 7 people or objects taken 4 at a time is
written P/7. 1). The expression for the softball lineup above is a case of
the following formula
ading Math
KEY CONCEPT
Permutations
The number of permutations of n distinct objects taken r at a time is given by
PC ) –
mutations The
ression and neads