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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 =
E Birbeck 7/[email protected]
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 =
E Birbeck 7/[email protected]
Odds versus Probability
Chances of success
Chances of failure Odds of success =
Chances of failure
Chances of success Odds of failure =
# of ways a certain outcome can occur
# of possible outcomes Probability =
E Birbeck 7/[email protected]
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
# of ways a certain outcome can occur
# of possible outcomes Probability =
E Birbeck 7/[email protected]
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
# of ways a certain outcome can occur# of ways a certain outcome can occur
# of possible outcomes Probability =
4 ways
E Birbeck 7/[email protected]
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 4 ways
4 # of possible outcomes
Probability =
E Birbeck 7/[email protected]
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 4 ways
4
# of possible outcomes# of possible outcomes Probability =
6 outcomes
E Birbeck 7/[email protected]
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 4 ways
4
# of possible outcomes# of possible outcomes Probability =
6 outcomes
E Birbeck 7/[email protected]
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 4 ways
4
6 Probability =
6 outcomes
E Birbeck 7/[email protected]
4
6 Probability =
What is the probability of rolling a factor of 6 on a six sided die?
Question
Simplify4
6= 2
3
The probability of rolling a factor of 6 on a
six sided die is . 2
3
E Birbeck 7/[email protected]
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?
E Birbeck 7/[email protected]
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.
E Birbeck 7/[email protected]
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
E Birbeck 7/[email protected]
Practice:
Playing Monopoly or Backgammon, you get to roll again if you roll doubles. What is the probability of rolling doubles?
# of ways a certain outcome can occur
# of possible outcomes Probability =
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.
E Birbeck 7/[email protected]
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
E Birbeck 7/[email protected]
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.
E Birbeck 7/[email protected]
There are 6 ways to get doubles. There 36 possible outcomes.
# of ways a certain outcome can occur
# of possible outcomes Probability =
E Birbeck 7/[email protected]
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
# of possible outcomes Probability =
E Birbeck 7/[email protected]
There are 6 ways to get doubles. There 36 possible outcomes.
6
# of possible outcomes Probability =
E Birbeck 7/[email protected]
There are 6 ways to get doubles. There 36 possible outcomes.
6
# of possible outcomes# of possible outcomes Probability =
E Birbeck 7/[email protected]
There are 6 ways to get doubles. There 36 possible outcomes.
6
36 Probability =
E Birbeck 7/[email protected]
There are 6 ways to get doubles. There 36 possible outcomes.
6
36 Probability =
Simplify 6
36=
1
6
What is the probability of rolling doubles?
Question:
The probability of rolling doubles is .
1
6
E Birbeck 7/[email protected]
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
E Birbeck 7/[email protected]
Probability
# of ways a certain outcome can occur
# of possible outcomes Probability =
The probability of an event is always between 0 and 1 or 0-100%.
Odds and Probability are expressed differently.
*
*
*
E Birbeck 7/[email protected]
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
E Birbeck 7/[email protected]
b) Find the probability of selecting an M if 28 tiles have been chosen and one of them was an M.
# 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
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).
E Birbeck 7/[email protected]
c) Find the probability of selecting an X if 42 tiles have been chosen and one of them was an X.
# 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
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
E Birbeck 7/[email protected]
P(selecting an E) = 12
100or
3
25
Convert the fractions to percents.
P(selecting an M) = 1
72
P(selecting an X) = 0
58 or 0
12%
0%
impossible
E Birbeck 7/[email protected]
Convert the fractions to percents.
1
72P(selecting an M) =
1.4%
1 ÷ 72means
1 ÷ 72 = 0.0138 = 1.38%= 1.4%
E Birbeck 7/[email protected]
P(selecting an E) = 12
100or
3
25
Convert the fractions to percents.
P(selecting an M) = 1
72
P(selecting an X) = 0
58 or 0
12%
0%
impossible
1 ÷ 72 1.4%
E Birbeck 7/[email protected]
Probability
# of ways a certain outcome can occur
# of possible outcomes Probability =
The probability of an event is always between 0 and 1 or 0-100%.
Odds and Probability are expressed differently.
*
*
*
E Birbeck 7/[email protected]
Probability
# of ways a certain outcome can occur
# of possible outcomes Probability =
The probability of an event is always between 0 and 1 or 0-100%.
Odds and Probability are expressed differently.
*
*
*
E Birbeck 7/[email protected]