1. The Basics of Probability

Question 1

What is a Probability Frequency Distribution?

Question 2

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.

Question 3

What is Probability?

Answer 3

Is the chance of something happening.

The likelihood of an event occurring

Question 4

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

Answer 4

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

Question 5

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

Question 6

How are Probabilities expressed?

Answer 6

Numerically - usually written out, between 0-1

Question 7

What does a probability of 1 represent?

Answer 7

The absolute certainty of the event occuring.

Question 8

What does a probability of 0 represent?

Answer 8

The absolute certainty of the event NOT occurring

Question 9

Higher probability values represent what?

Answer 9

A higher likelihood

Question 10

How is Event A denoted?

Answer 10

P (A)

Question 11

What is P (A) equal to?

Answer 11

the number of preferred outcomes / total number of possible outcomes

all

Question 12

What is another term to depict all possible outcomes?

Answer 12

Sample space

Question 13

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

Answer 13

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

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

Question 14

Why do we express probabilities numerically?

Answer 14

To compare which event is relatively more likely.

Question 15

Define Expected Values

Answer 15

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

Question 16

What is an Experiment?

Answer 16

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

Question 17

What are the Probabilities called after we conduct experiments?

Answer 17

Experimental Probabilities

Question 18

What is another type of Probabilities?

Answer 18

Theoretical (or true) probabilities

Question 19

What is the formula for Experimental Probabilities?

Answer 19

P (A) = successful trials / all trials

Question 20

What is the Expected Value of an event?

Answer 20

The outcome we expect to occur when we run an experiment

denoted as:
E (A)

Question 21

Why do we use experimental probabilities?

Answer 21

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

Question 22

When is the Expected Value used?

Answer 22

When trying to predict future events

Question 23

What is a Probability Frequency Distribution?

Answer 23

A collection of the probabilities for each possible outcome

Question 24

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

Answer 24

divide the frequencies by the size of the sample space

Question 25

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

Answer 25

a Probability Frequency Distribution

Question 26

What is the opposite of an Event?

Answer 26

A Complement

Question 27

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

Answer 27

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

Question 28

What is a Complement of an Event?

Answer 28

Everything the event is not

a complement helps complete the rest of the sample space

Question 29

The sum of all probabilities should equal what number?

Answer 29

1 this is equal to 100%

Question 30

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

Answer 30

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

Question 31

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

Answer 31

We can not accounted for one or several possible outcomes

Question 32

What does probability express?

Answer 32

the likelihood of an event occurring

Question 33

Do all events have complements?

Answer 33

Yes

Question 34

How are complements denoted?

Answer 34

With an apostrophe - A’

Question 35

What is an example of a complement?

Answer 35

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

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

Question 36

When are complements often used?

Answer 36

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

Question 37

How are complements calculated?

Answer 37

P(A’) = 1 - P(A)

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

Question 38

What is the complement of NOT rolling a 3?

Answer 38

Rolling a 3