A2HardingSpring15Day1­Probability.notebook
December 03, 2015
Algebra 2
Ch.12 Notes Page 58
P58 1­6 Basic Probability
9­7 Probability of Multiple Events
12­2 Conditional Probability
Aug 19­6:20 AM
1­6 Probability
Probability
What are the chances that some event will occur?
Probability (Event) = Favorable Outcomes
Total Outcomes
Example: Rolling an Even Number on a Number Cube
Jan 20­8:27 AM
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A2HardingSpring15Day1­Probability.notebook
December 03, 2015
Experimental Probability
What does happen when you do the experiment.
(If you toss the coin 100 times, you might get 60 heads and 40 tails.)
Flipping a Coin (Results = H, T, H, T, H)
Rolling a Die (Result = 1,3,4,5,5,5,5,6)
Apr 27­9:01 AM
Theoretical Probability
What should happen if the experiment is done over and over again.
Tossing a coin.
(Should be 50% Heads and 50% Tails)
Apr 27­9:01 AM
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A2HardingSpring15Day1­Probability.notebook
December 03, 2015
Sample Space
Sample Space ­ The set of all possible outcomes
All Outcomes
Specific Event
Apr 27­9:01 AM
Geometric Probability
Geometric Probability ­ Uses Areas/Lengths/Time to find Probability
P(Landing on the Circle)
3
10
40
Apr 27­9:01 AM
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A2HardingSpring15Day1­Probability.notebook
December 03, 2015
9­7 Probability of Multiple Events
Marbles ­ 2 Green 5 Red 3 Blue
P (A and B) = P(A) x P(B)
Dependent events ­
One event affects the outcome of a second event
P(G and R) Without Replacement
Independent Events ­
One event does not affect the outcome of a second event
P(G and R) With Replacement
Apr 27­9:03 AM
Mutually Exclusive Events ­ Two events that cannot happen at the same time.
If A and B are Mutually Exclusive, P (A and B) = 0
Example: Rolling an even number and a number less than 2 on a 6 sided die.
Apr 27­9:03 AM
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A2HardingSpring15Day1­Probability.notebook
December 03, 2015
Probability of A or B
If A and B are mutually exclusive ­ P (A or B) = P(A) + P(B)
Standard Die
P (3 or even) = 1/6 + 1/2 = 4/6 = 2/3
If A and B are not mutually exclusive ­ P (A or B) = P(A) + P(B) ­ P(A and B)
Standard Die
P (3 or odd) = 1/6 + 1/2 ­ 1/6 = 1/2
Apr 27­9:03 AM
12­2 Conditional Probability
Contains a condition that might limit the sample space.
P (B | A) = Probability of event B, given event A
P (B | A) = P (A and B)
P(A)
P (Did Homework | Male)
Male
Female
= 8/14 = 4/7
Yes HW No HW
8
6 12
4
14
16
Apr 27­9:03 AM
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A2HardingSpring15Day1­Probability.notebook
December 03, 2015
Tree Diagrams
On 28% of the days, the sky is clear.
On Clear days, it rains 4% of the time.
On Cloudy days, it rains 32% of the time.
Find the Probability it will be clear, but rain.
Apr 27­9:03 AM
(In Class)???
1­6 P42 #1,6,7,10,11,17
9­7 P534 #1,2,5,6,10,11,14,15,18,19,24,25,36
12­2 P656 #1­8,11,12
Please put your name and class period at the top of the homework. Also include the homework number.
Aug 19­6:25 AM
6