9.7 Probability

Mutually exclusive events

Definition of Probability

Probability is the Outcomes divided by Sample Space.

Outcomes the results of some event.

Sample Space is all the possible results of some event.

To see this lets look at dice

How many different ways can fair 6 sided dice be rolled?

Here are the pairs ( first die, second die )

(1,1), (2,1), (3,1), (4,1), (5, 1), (6, 1)

(1,2), (2,2), (3,2), (4,2), (5, 2), (6,2)

(1,3), (2,3), (3,3), (4,3), (5, 3), (6,3)

(1,4), (2,4), (3,4), (4,4), (5, 4), (6,4)

(1,5), (2,5), (3,5), (4,5), (5, 5), (6,5)

(1,6), (2,6), (3,6), (4,6), (5, 6), (6,6)

36 ways “Sample Space”

How many different ways can fair 6 sided dice be rolled to add to 7?

Here are the pairs ( first die, second die )(1,1), (2,1), (3,1), (4,1), (5, 1), (6, 1)(1,2), (2,2), (3,2), (4,2), (5, 2), (6,2) (1,3), (2,3), (3,3), (4,3), (5, 3), (6,3)(1,4), (2,4), (3,4), (4,4), (5, 4), (6,4)(1,5), (2,5), (3,5), (4,5), (5, 5), (6,5)(1,6), (2,6), (3,6), (4,6), (5, 6), (6,6)

6 ways Outcome

The Probability of rolling a seven with fair 6 sided dice

Using the equation.Outcome is n(E); Sample Space is n(S)

Probability is always between 0 and 1.0 probability never going to happen. 1 probability always going to happen.

%6.16

36

6

Sn

EnEP

Mutually Events

If you needed to count all the student taking Algebra 2c or Geometry, you would take the class list and add the number of students together.

Algebra 2c has 97 students

Geometry has 116 students

Total 213 students

Mutually Events

If you needed to count all the student taking Algebra 2c or Geometry, you would take the class list and add the number of students together. Yet you need to remember some students are in both classes, they would need to be subtracted.

Students taking both Algebra 2c and Geometry at the same time is 18 students.

Mutually Events

You need the number students in Algebra 2c or Geometry.

Algebra 2c Students 97

Geometry Students 116 Total 213

Students who are taking both classes 18

Subtract

Students taking Algebra 2c or Geometry 195

Independent Events

The Probability of independent events are their individual probabilities multiplied together.

What is the possible of rolling a 3 with 3 dice? All the dice would have to be 1.

First, second and third dice probability of a one is

The probability would be 6

1

216

1

6

1

6

1

6

1

The Complement of an Event

Given a probability of something happening, then the probability of something not happening is 100% - the probability.

If there was 40 % chance of rain, there is a 60% chance of it not raining.

Homework

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36, 46, 58