probability Flashcards

1
Q

what does probability study

A

Probability studies randomness and is a quantity between 0 and 1, sometimes expressed as a percentage.

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2
Q

what are proportions

A

A number, amount, or level of one thing when compared to another, expressed between [0,1] or as a percentage.

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3
Q

How is mathematical probability calculated?

A

By dividing the number of favorable outcomes by the total number of possible outcomes.
The total number of possible outcomes is the sample space.

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4
Q

what is empirical probability

A

The proportion of favourable outcomes observed in a sample .

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5
Q

what is relative frequency

A

The proportion of favorable outcomes in a sample, approaching a limit as sample size increases.

As sample size increases, the relative frequency will reach a limit.

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6
Q

what is the complement rule

A

The probability of an event NOT occurring is:

Pr(𝑋′)=1βˆ’Pr⁑(𝑋)

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7
Q

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

A

1/6

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8
Q

multiplication rule

A

For two independent events 𝑋 and π‘Œ, the probability of of both occurring is: π‘ƒπ‘Ÿ(π‘‹βˆ©π‘Œ)=π‘ƒπ‘Ÿ(𝑋)Γ—π‘ƒπ‘Ÿ(π‘Œ)

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9
Q

What is the probability of flipping a Head AND rolling a 6?

A

π‘ƒπ‘Ÿ(π‘‹βˆ©π‘Œ) = 1/2 x 1/6 = 1/12

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10
Q

what does it mean if events X and Y are independent

A

If 𝑋 and π‘Œ are independent one event does not influence another.

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11
Q

what does ∩ stand for

A

AND

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12
Q

What is the addition rule in probability?

A

The probability of event 𝑋 OR event Y OR BOTH occurring is:

π‘ƒπ‘Ÿ(𝑋βˆͺπ‘Œ)=π‘ƒπ‘Ÿ(𝑋)+π‘ƒπ‘Ÿ(π‘Œ)βˆ’π‘ƒπ‘Ÿ(π‘‹βˆ©π‘Œ)

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13
Q

What is the probability of flipping a Head OR rolling a 6 OR both?

A

π‘ƒπ‘Ÿ(𝑋βˆͺπ‘Œ)= 1/2 + 1/6 - 1/12 = 7/12

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14
Q

what does βˆͺ mean

A

union
a OR b
BOTH a & b

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15
Q

what does it mean if events X and Y are not mutually exclusive

A

the two events can happen together

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16
Q

What are mutually exclusive events?

A

events that cannot occur at the same time. For example, a coin cannot show both heads and tails at the same time.

P(X∩Y)=0

17
Q

if events X and Y are mutually exclusive what happens to the multiplication and addition rule

A

π‘ƒπ‘Ÿ(π‘‹βˆ©π‘Œ)=0

π‘ƒπ‘Ÿ(𝑋βˆͺπ‘Œ)=π‘ƒπ‘Ÿ(𝑋)+π‘ƒπ‘Ÿ(π‘Œ)

18
Q

what is conditional probabilitiy

A

Conditional probability is the probability of event 𝐴 occurring given that event 𝐡 has already occurred

19
Q

formula for conditional probability

A

π‘ƒπ‘Ÿ(𝑋|π‘Œ) = π‘ƒπ‘Ÿ(π‘‹βˆ©π‘Œ) / π‘ƒπ‘Ÿ(π‘Œ)

20
Q

How do you calculate the probability of two dependent events?

A

π‘ƒπ‘Ÿ(π‘‹βˆ©π‘Œ)=π‘ƒπ‘Ÿ(𝑋|π‘Œ)Γ—π‘ƒπ‘Ÿ(π‘Œ)

21
Q

what are non independent events

A

If 𝑋 and π‘Œ are independent then π‘ƒπ‘Ÿ(𝑋|π‘Œ)=π‘ƒπ‘Ÿ(𝑋)

22
Q

what is bayes theorum

A

Bayes’ Theorem provides a way to update the probability of an event based on new information:
π‘ƒπ‘Ÿ(𝑋|π‘Œ) = [π‘ƒπ‘Ÿ(π‘Œ|𝑋)π‘ƒπ‘Ÿ(𝑋)] / π‘ƒπ‘Ÿ(π‘Œ)

23
Q

how to convert numbers to proportions

A

divide by the total sample

24
Q

What is marginal probability?

A

Marginal probability is the probability of an event occurring, regardless of other variables.

25
Q

What is joint probability?

A

Joint probability is the probability of two events happening at the same time

26
Q

What is the complement rule in probability?

A

The complement rule states that the probability of an event not occurring is:
P(Β¬X)=1βˆ’P(X)

27
Q

What are the basic probability rules?

A

Complement rule
Addition rule
Multiplication rule
Conditional probability