Probability

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Frequentist Approach

Probabilities can be thought of as frequencies

ex.

number of correct options/number of total options

ex.

1/2 for probability of getting heads

Your team won 9 out of 12 games

Frequency of wining: 9

Relative Frequency of winning: 75%

Ex: 62 out of 100 days it rains in Seattle. Therefore any random day has as 62 percent chance or raining

However, it rains les on August 1

You also have to take in to account humidity, wind direction, and the weather

Subjective vs Frequency probability

Subjective: it could be a 6 or a 9. It is changed based on a person's opinion

Frequency: is Objective and doesn't change

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Different Probabilities

You say there is a 1/6th probability of getting a six when rolling a die. But your friend says that the prob is a 2/3. Even if when you roll it to your friend, you are still right and your friend is still wrong.

P(A) A= Random baby being a girl

P(A): 0.510

Symmetrical outcomes

A di has 6 sides, each side has the same change

Heads or tails = all options have the same chance

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We will normally use the frequentist approach and are non-dogmatic (not 0 or 1)

P(the sun comes up)<1

P(alien invasion) >0

Subjective Approach

Non symmetrical or non-frequency

assigning probabilities to events that reflect personal opinion

Such an approach to probability loses the objective content of the idea of change; probability becomes an opinion

Frequentist Approach

Almost always neither 0 or 1

0= will never happen. 1= will for certain happen

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Union and Instersection

A u b: an y one that fufills one of them

A upside down u: Fufills both

find union a b and c 4 tomorrow

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Union and Intersection

Ex.

2 dice.

A: P that the 2 numbers will be the same

B: P that the sum is greater than 8

Union of a and b: 2,2 3,3 4,4

Intersection of a and b: 5, 5 and 6,6

number of events in a union

n(A u B) = n(A)+n(B)-N(intersection of A and B)

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