1. The Basics of Probability Flashcards
What is a Probability Frequency Distribution?
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.
What is Probability?
Is the chance of something happening.
The likelihood of an event occurring
What does the word ‘event’ mean when talking about probabilities?
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
we want to measure and compare probabilities in order to know which event is more likely
How are Probabilities expressed?
Numerically - usually written out, between 0-1
What does a probability of 1 represent?
The absolute certainty of the event occuring.
What does a probability of 0 represent?
The absolute certainty of the event NOT occurring
Higher probability values represent what?
A higher likelihood
How is Event A denoted?
P (A)
What is P (A) equal to?
the number of preferred outcomes / total number of possible outcomes
all
What is another term to depict all possible outcomes?
Sample space
What is the formula for calculating the probability of two independent events occurring?
P (A and B) = P (A) * P (B)
Example:
P (Ace of Spades) = P (Ace) * P (Spade)
Why do we express probabilities numerically?
To compare which event is relatively more likely.
Define Expected Values
Expected Values are the average outcome we expect if we run an experiment many times
What is an Experiment?
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
What are the Probabilities called after we conduct experiments?
Experimental Probabilities
What is another type of Probabilities?
Theoretical (or true) probabilities
What is the formula for Experimental Probabilities?
P (A) = successful trials / all trials
What is the Expected Value of an event?
The outcome we expect to occur when we run an experiment
denoted as:
E (A)
Why do we use experimental probabilities?
Because they are easy to compute AND serve as good predictors for theoretical ones.
When is the Expected Value used?
When trying to predict future events
What is a Probability Frequency Distribution?
A collection of the probabilities for each possible outcome
How to you calculate the probabilities from a frequency distribution table?
divide the frequencies by the size of the sample space
A collection of the probabilities for the various outcomes in a frequency distribution table is called?
a Probability Frequency Distribution
What is the opposite of an Event?
A Complement
What does the frequency of a value within the sample space represent?
The number of times the value features in the sample space.
What is a Complement of an Event?
Everything the event is not
a complement helps complete the rest of the sample space
The sum of all probabilities should equal what number?
1 this is equal to 100%
What if we have the sum of probabilities greater than 1?
This can occur when some of the assumed outcome can occur simultaneously.
we are double counting some of the possible outcomes
What happens when we end up with a sum of probabilities less than 1?
We can not accounted for one or several possible outcomes
What does probability express?
the likelihood of an event occurring
Do all events have complements?
Yes
How are complements denoted?
With an apostrophe - A’
What is an example of a complement?
Rolling a die - if you wanted to roll an even number
A => rolling an even number
A’ => not rolling an even number
When are complements often used?
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
How are complements calculated?
P(A’) = 1 - P(A)
The probability of the inverse (complement) = 1 - the probability of the event itself
What is the complement of NOT rolling a 3?
Rolling a 3
