E Birbeck 7/04

1
Simple Probability

• Definition
  Probability the chance some
  event will happen. It is the ratio of the number
  of ways an event can occur to the number of
  possible outcomes.

of ways a certain outcome can occur
of possible outcomes
2
Clarification Caution
Odds versus Probability
The ratio for odds uses chances of success and
chances of failurenot the total number of
outcomes.
Chances of success
Odds of success
Chances of failure
Chances of failure
Odds of failure
Chances of success
3
Clarification Caution
Odds versus Probability
of ways a certain outcome can occur
Probability
of possible outcomes
4
Practice
What is the probability of rolling a factor of 6
on a six sided die?
Know

• A six sided die is labeled 1,2,3,4,5,6

• A factor of 6 is a whole number that divides
  evenly into 6

1 x 6 6 2 x 3 6
Factors of 6
1, 2, 3, 6
of ways a certain outcome can occur
Probability
of possible outcomes
5
Practice
What is the probability of rolling a factor of 6
on a six sided die?
Know

• A six sided die is labeled 1,2,3,4,5,6

• A factor of 6 is a whole number that divides
  evenly into 6

1 x 6 6 2 x 3 6
Factors of 6
1, 2, 3, 6
4 ways
of ways a certain outcome can occur
Probability
of possible outcomes
6
Practice
What is the probability of rolling a factor of 6
on a six sided die?
Know

• A six sided die is labeled 1,2,3,4,5,6

• A factor of 6 is a whole number that divides
  evenly into 6

1 x 6 6 2 x 3 6
Factors of 6
1, 2, 3, 6 4 ways
4
Probability
of possible outcomes
7
Practice
What is the probability of rolling a factor of 6
on a six sided die?
Know

• A six sided die is labeled 1,2,3,4,5,6

6 outcomes

• A factor of 6 is a whole number that divides
  evenly into 6

1 x 6 6 2 x 3 6
Factors of 6
1, 2, 3, 6 4 ways
4
Probability
of possible outcomes
8
Practice
What is the probability of rolling a factor of 6
on a six sided die?
Know

• A six sided die is labeled 1,2,3,4,5,6

6 outcomes

• A factor of 6 is a whole number that divides
  evenly into 6

1 x 6 6 2 x 3 6
Factors of 6
1, 2, 3, 6 4 ways
4
Probability
of possible outcomes
9
Practice
What is the probability of rolling a factor of 6
on a six sided die?
Know

• A six sided die is labeled 1,2,3,4,5,6

6 outcomes

• A factor of 6 is a whole number that divides
  evenly into 6

1 x 6 6 2 x 3 6
Factors of 6
1, 2, 3, 6 4 ways
4
Probability
6
10
Question
What is the probability of rolling a factor of 6
on a six sided die?
Simplify

The probability of rolling a factor of 6 on a
six sided die is .
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What does that mean?
Two out of three times that you roll the dice,
you should roll a factor of 6. 66.6
67 of the time you should roll a
factor of 6.
12
What does that mean? Two out of three times that
you roll the dice, you should roll a factor of
6. 66.6
67 of the time you should roll a
factor of 6.
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Sample Space

• Definition
  Sample Space the set of all
  possible outcomes

Sample Space is used to create a chart or table
to solve the problem.
When flipping a coin, the sample space is heads
or tails.
heads tails
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Practice
Playing Monopoly or Backgammon, you get to roll
again if you roll doubles. What is the
probability of rolling doubles?
Know
of ways a certain outcome can occur
Probability
of possible outcomes
Each die has 6 sides
Solve
Make a table showing all the combinations that
you could roll on a pair of dice as ordered pairs.
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Sample Space for Rolling two Die
Second die
1 2 3 4
5 6
Fi rs t d ie
1 2 3 4 5 6
(1,1) (1,2) (1,3) (1,4)
(1,5) (1,6)
(2,1) (2,2) (2,3) (2,4)
(2,5) (2,6)
(3,1) (3,2) (3,3) (3,4)
(3,5) (3,6)
(4,1) (4,2) (4,3) (4,4)
(4,5) (4,6)
(5,1) (5,2) (5,3) (5,4)
(5,5) (5,6)
(6,1) (6,2) (6,3) (6,4)
(6,5) (6,6)
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There are 6 ways to get doubles. There 36
possible outcomes.
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There are 6 ways to get doubles. There 36
possible outcomes.
of ways a certain outcome can occur
Probability
of possible outcomes
18
There are 6 ways to get doubles. There 36
possible outcomes.
of ways a certain outcome can occur
Probability
of possible outcomes
19
There are 6 ways to get doubles. There 36
possible outcomes.
6
Probability
of possible outcomes
20
There are 6 ways to get doubles. There 36
possible outcomes.
6
Probability
of possible outcomes
21
There are 6 ways to get doubles. There 36
possible outcomes.
6
Probability
36
22
There are 6 ways to get doubles. There 36
possible outcomes.
6
Probability
36
Question
What is the probability of rolling doubles?
Simplify

The probability of rolling doubles is .

23
The probability of an event is always
between 0 and 1, inclusive. If an event cannot
happen, its probability is 0. If something is
certain to happen, its probability is 1
0
1
impossible
certain
50-50 chance
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0
1
impossible
certain
50-50 chance
100
50
0
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Probability
of ways a certain outcome can occur
Probability

of possible outcomes
Odds and Probability are expressed differently.

The probability of an event is always between
0 and 1 or 0-100.

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Practice In Scrabble, each player chooses seven
letter tiles. The 100 tiles
are in the distribution table below.
of tiles
Letters
1
J, K, Q, X, Z
a) Find the probability of selecting an E if no
tiles have been chosen.
B, C, F, H, M, P, V, W, Y, blank
2
G
3
D,L,S,U
4
Know There are 12 E tiles and 100 tiles in all.
N,R,T
6
O
8
A,I
9
E
12
P(selecting an E)
or
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Scrabble Breakdown
b) Find the probability of selecting an M if 28
tiles have been chosen and one of them was an M.
Know There are 2 M tiles. 1 has
been selected, so 1 positive outcome remains.
There are 100 - 28 72 tiles left (72 possible
outcomes).
P(selecting an M)
28
Scrabble Breakdown
c) Find the probability of selecting an X if 42
tiles have been chosen and one of them was an X.
Know There is only 1 X tile. 1 has
been selected, so 0 positive outcomes remain.

There are 100 - 42 58 tiles left (58 possible
outcomes).
or 0
P(selecting an X)
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Convert the fractions to percents.
12
0
impossible
30
Convert the fractions to percents.
1.4
means
1 72
1 72 0.0138
1.4
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Convert the fractions to percents.
12
1 72
1.4
0
impossible
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Probability
of ways a certain outcome can occur
Probability

of possible outcomes
Odds and Probability are expressed differently.

The probability of an event is always between
0 and 1 or 0-100.

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Probability
of ways a certain outcome can occur
Probability

of possible outcomes
Odds and Probability are expressed differently.

The probability of an event is always between
0 and 1 or 0-100.

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