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365 Data Science - Probability > 1. The Basics of Probability > Flashcards

1. The Basics of Probability Flashcards

1
Q

What is a Probability Frequency Distribution?

A
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2
Q

What is the chance of success? What is the possibility that we fail? To determine if the risk is worth taking.

by using probability and statistical data, CEO’s can predict how likely each outcome is and make the right call for their company.

A
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3
Q

What is Probability?

A

Is the chance of something happening.

The likelihood of an event occurring

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4
Q

What does the word ‘event’ mean when talking about probabilities?

A

an event is a specific outcome or a combination of serval outcomes

example:
flipping coins (heads or tails) has two possible events and we need to assign probabilities to each event

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5
Q

we want to measure and compare probabilities in order to know which event is more likely

A
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6
Q

How are Probabilities expressed?

A

Numerically - usually written out, between 0-1

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7
Q

What does a probability of 1 represent?

A

The absolute certainty of the event occuring.

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8
Q

What does a probability of 0 represent?

A

The absolute certainty of the event NOT occurring

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9
Q

Higher probability values represent what?

A

A higher likelihood

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10
Q

How is Event A denoted?

A

P (A)

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11
Q

What is P (A) equal to?

A

the number of preferred outcomes / total number of possible outcomes

all

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12
Q

What is another term to depict all possible outcomes?

A

Sample space

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13
Q

What is the formula for calculating the probability of two independent events occurring?

A

P (A and B) = P (A) * P (B)

Example:
P (Ace of Spades) = P (Ace) * P (Spade)

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14
Q

Why do we express probabilities numerically?

A

To compare which event is relatively more likely.

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15
Q

Define Expected Values

A

Expected Values are the average outcome we expect if we run an experiment many times

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16
Q

What is an Experiment?

A

a group of multiple trials

example:
Tossing a coin to see it’s outcome = a trial
if we toss a coin 20x and recored 20 outcomes - this process is a single experiment with 20 trials

17
Q

What are the Probabilities called after we conduct experiments?

A

Experimental Probabilities

18
Q

What is another type of Probabilities?

A

Theoretical (or true) probabilities

19
Q

What is the formula for Experimental Probabilities?

A

P (A) = successful trials / all trials

20
Q

What is the Expected Value of an event?

A

The outcome we expect to occur when we run an experiment

denoted as:
E (A)

21
Q

Why do we use experimental probabilities?

A

Because they are easy to compute AND serve as good predictors for theoretical ones.

22
Q

When is the Expected Value used?

A

When trying to predict future events

23
Q

What is a Probability Frequency Distribution?

A

A collection of the probabilities for each possible outcome

24
Q

How to you calculate the probabilities from a frequency distribution table?

A

divide the frequencies by the size of the sample space

25
Q

A collection of the probabilities for the various outcomes in a frequency distribution table is called?

A

a Probability Frequency Distribution

26
Q

What is the opposite of an Event?

A

A Complement

27
Q

What does the frequency of a value within the sample space represent?

A

The number of times the value features in the sample space.

28
Q

What is a Complement of an Event?

A

Everything the event is not

a complement helps complete the rest of the sample space

29
Q

The sum of all probabilities should equal what number?

A

1 this is equal to 100%

30
Q

What if we have the sum of probabilities greater than 1?

A

This can occur when some of the assumed outcome can occur simultaneously.
we are double counting some of the possible outcomes

31
Q

What happens when we end up with a sum of probabilities less than 1?

A

We can not accounted for one or several possible outcomes

32
Q

What does probability express?

A

the likelihood of an event occurring

33
Q

Do all events have complements?

A

Yes

34
Q

How are complements denoted?

A

With an apostrophe - A’

35
Q

What is an example of a complement?

A

Rolling a die - if you wanted to roll an even number

A => rolling an even number
A’ => not rolling an even number

36
Q

When are complements often used?

A

When the event we want to occur is satisfied by many outcomes

ie. you want to know the probability to rolling a 1, 2, 4, 5, 6
is the same as
the probability of not rolling a 3

37
Q

How are complements calculated?

A

P(A’) = 1 - P(A)

The probability of the inverse (complement) = 1 - the probability of the event itself

38
Q

What is the complement of NOT rolling a 3?

A

Rolling a 3

365 Data Science - Probability (6 decks)

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