Transcript Probability Unit Notes

COUNTING OUTCOMES
P E R M U TAT I O N S & C O M B I N AT I O N S
P RO BA B I L I T Y
REVIEW
8/21
COUNTING OUTCOMES
Andy has 3 pairs of pants: 1 gray, 1 blue and 1 black. He
has 2 shirts: 1 white and 1 red. If Andy picks 1 pair of
pants and 1 shirt, how many different outfits does he have?
Andy can choose 1 of 3 pairs of pants and 1 of 2 shirts. A
tree diagram can help you count his choices.
The total number of choices is the product of the number
of choices for item A, the number of choices for item B, etc.
You can also use the counting principle.
FIRST ● SECOND ● THIRD, etc. = TOTAL NUMBER
OF CHOICES
FIND THE TOTAL NUMBER
OF CHOICES.
1. Moesha has 6 pairs of socks and 2 pairs of
sneakers. She chooses 1 pair of socks and 1
pair of sneakers. How many possible
combinations are there?
2. Kim has 5 swimsuits, 3 pairs of sandals, and
2 beach towels. In how many ways can she pick
one of each to go to the beach with?
PERMUTATIONS
The expression 5! is read “5 factorial”.
It means the product of all whole numbers from
5 to 1.
5! =
Evaluate
5!

3!
How many 3-letter codes can be made from A, B,
C, D, E, F, G, H with no repeating letters?
This is a permutation problem. ORDER IS
IMPORTANT. ABC is different from ACB.
• There are
• There are
• There are
choices for the first letter.
choices for the second letter.
choices for the third letter.
PERMUTATION FORMULA
n
Pr
 n is the number of objects and r is the number chosen.
can write the code as 8 P3 ,
meaning the number of permutations
of 8 objects chosen at 3 times.
You

The number of codes possible
x
x
=
Evaluate each factorial.
1. 4!
2. 7!
8!
3.
3!
4. 5!  2!
Find the value of each expression.
5. 6 P3
6. 5 P2
7. 12 P3
8. 15 P4
Solve.
9. In how many ways can
you pick a football center
and quarterback from 6
players who try out?
10. For a meeting agenda,
in how many ways can you
schedule 3 speakers out of
10 people who would like to
speak?
COMBINATIONS
Mr. Jones wants to pick 2 students from Martin, Joan,
Bart, Esperanza, and Tina to demonstrate an
experiment. How many different pairs of students can
he choose?
In this combination problem, the ORDER DOES
NOT MATTER. What are the possibilities?
There are
possible combinations.
COMBINATION FORMULA
n Pr
n Cr 
r!
n is the number of objects and r is the number chosen
The number of combinations of 5 students taken 2 at
a time is:
5
C2 


FIND THE NUMBER OF
COMBINATIONS:
1. 6 C3
2. 9 C 4
3. 7 C5
4. 4 C3
Solve.
5. In how many ways
can Susie choose 3 of
10 books to take with
her on a trip?
6. In how many ways
can Rosa select 2
movies to rent out of 6
that she likes?
8/19
Probability:
• Notation: P(event)
Theoretical Probability:
• The likelihood of an event occurring.
• Equation: # of favorable outcomes
# of total outcomes
 Experimental Probability:
• The number of times an event occurs in an experiment.
• Equation: # of trials an outcome occurs
total # of trials
DEPENDENT EVENT INDEPENDENT EVENT
Spinning a spinner, and
then rolling a dice
Draw a card, keep it, then
drawing another card.
An event who’s
outcome is based on a
previous outcome.

An event who’s
outcome is NOT
based on a previous
outcome.
WITH REPLACEMENT
P(A and B) = P(A) • P(B)
A bag of marbles contains 6 blue, 5 red, 3 green, 4 orange, and 2
purple. You draw a marble at random, record your findings, replace
the marble, then draw again.
Find
3 3
9
Ex) P(blue, blue) = 10  10  100
You Try
a) P(purple, orange) =
b) P(black, blue) =
WITHOUT REPLACEMENT
P(A and B after A) = P(A) • P(B after A)
A sock drawer contains 4 black, 2 yellow, 3
polk-a-dot, 5 Nike, and 6 pink. You pick a
sock at random, record your findings, then
pick another without replacing the first.
Find
Ex) P(yellow, pink) =
You Try
a) P(black, black) =
1 6
3
 
10 19 95
b) P(Nike, pink) =