e birbeck 7/04 [email protected] simple probability definition: probability : the chance some...

E Birbeck 7/[email protected]

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 outcomesProbability =


Odds versus Probability

Chances of success

Chances of failure Odds of success =

The ratio for odds uses chances of success and chances of failure…not the total number of outcomes.

Chances of failure

Chances of success Odds of failure =


Odds versus Probability

Chances of success

Chances of failure Odds of success =

Chances of failure

Chances of success Odds of failure =


# of possible outcomes Probability =


Practice:

What is the probability of rolling a factor of 6 on a six sided die?

•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

Know:

Factors of 61 x 6 = 6 2 x 3 = 6

1, 2, 3, 6




Practice:




Know:

Factors of 61 x 6 = 6 2 x 3 = 6

1, 2, 3, 6

# of ways a certain outcome can occur# of ways a certain outcome can occur


4 ways


Practice:




Know:

Factors of 61 x 6 = 6 2 x 3 = 6

1, 2, 3, 6 4 ways

4 # of possible outcomes

Probability =


Practice:




Know:

Factors of 61 x 6 = 6 2 x 3 = 6

1, 2, 3, 6 4 ways

4

# of possible outcomes# of possible outcomes Probability =

6 outcomes


Practice:




Know:

Factors of 61 x 6 = 6 2 x 3 = 6

1, 2, 3, 6 4 ways

4

6 Probability =

6 outcomes


4

6 Probability =


Question

Simplify4

6= 2

3

The probability of rolling a factor of 6 on a

six sided die is . 2

3


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.

What does that mean?


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.


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


Practice:

Playing Monopoly or Backgammon, you get to roll again if you roll doubles. What is the probability of rolling doubles?



Know:

Solve:Each die has 6 sides

Make a table showing all the combinations that you could roll on a pair of dice as ordered pairs.


1 2 3 4 5 6

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)

Fi rs t d ie

Second die

Sample Space for Rolling two Die


1 2 3 4 5 6

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)

Fi rs t d ie

Second die

Sample Space for Rolling two Die

There are 6 ways to get doubles. There 36 possible outcomes.



# of ways a certain outcome can occur# of ways a certain outcome can occur




6




6

# of possible outcomes# of possible outcomes Probability =



6

36 Probability =



6

36 Probability =

Simplify 6

36=

1

6

What is the probability of rolling doubles?

Question:

The probability of rolling doubles is .

1

6


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 11

2

impossible certain50-50 chance


0 11

2

impossible certain50-50 chance

100% 50% 0%


Probability



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

Odds and Probability are expressed differently.

*

*

*


Practice:

In Scrabble, each player chooses seven letter tiles. The 100 tiles are in the distribution table below.

a) Find the probability of selecting an E if no tiles have been chosen.

# of tiles Letters

1 J, K, Q, X, ZB, C, F, H, M, P, V, W, Y, blank

G

D,L,S,UN,R,TOA,I

E

2

3

4689

12

Know: There are 12 E tiles and 100 tiles in all.

P(selecting an E) = 12

100or

3

25


b) Find the probability of selecting an M if 28 tiles have been chosen and one of them was an M.

# of tiles Letters


G

D,L,S,UN,R,TOA,I

E

2

3

4689

12

Scrabble Breakdown

Know: There are 2 M tiles. 1 has been selected, so 1 positive outcome remains.

P(selecting an M) = 1

72

There are 100 - 28 = 72 tiles left (72 possible outcomes).


c) Find the probability of selecting an X if 42 tiles have been chosen and one of them was an X.

# of tiles Letters


G

D,L,S,UN,R,TOA,I

E

2

3

4689

12

Scrabble Breakdown

Know: There is only 1 X tile. 1 has been selected, so 0 positive outcomes remain.

P(selecting an X) = 0

58

There are 100 - 42 = 58 tiles left (58 possible outcomes).

or 0



100or

3

25

Convert the fractions to percents.


72


58 or 0

12%

0%

impossible



1

72P(selecting an M) =

1.4%

1 ÷ 72means

1 ÷ 72 = 0.0138 = 1.38%= 1.4%



100or

3

25



72


58 or 0

12%

0%

impossible

1 ÷ 72 1.4%


Probability



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

Odds and Probability are expressed differently.

*

*

*

e birbeck 7/04 [email protected] simple probability definition: probability : the chance some...

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