Probability Flashcards
(14 cards)
What is probability
A number between 0 and 1 (or 0% to 100%) that shows how likely something is to happen.
What is a random trial
A process or experiment that can have different outcomes and the result is not known in advance
What is an outcome
A single possible result of a random trial
What is an event
One or more outcomes that you care about
What does ‘mutually exclusive’ mean
Two (or more) events are mutually exclusive if they cannot happen at the same time.
What is the rule for mutually exclusive events
If A and B are mutually exclusive,
P(AandB) = 0 and P(AorB) = P(A)+ P(B)
What is a probability distribution
A probability distribution lists all possible outcomes and their associated probabilities
For discrete variables: a table or list
Total probability must = 1
What is a Probability Density Function (PDF)
A PDF is used for continuous random variables (like height or weight) where individual outcomes don’t have exact probabilities
Look at areas under the curve to get probabilities
Total area under the curve = 1
What is the general addition rule for probabilities
This rule is used to find the probability that either event A or B happens.
P(A∪B) =P(A) + P(B)− P(A∩B)
Use this rule when A and B can happen together (not mutually exclusive).
What does it mean if events are independent
Two events are independent if the outcome of one does not affect the other
What is the rule for two independent events
If A and B are independent
P(A∩B) = P(A) × P(B)
What is the general multiplication rule
This rule helps find the probability that both A and B happen, especially when they may not be independent
P(A∩B) = P(A) × P(B∣A)
Where
P(B∣A) = the probability of B happening given that A has happened
Use this rule when events are not independent
How do you use a probability tree
You multiply along the branches and add up the outcomes at the ends
What is the law of total probability
This law helps when an event’s probability depends on different conditions (or groups).
P(B)=P(B∣A1)P(A1) + P(B∣A2 )P(A2)+…
It breaks a problem into parts based on all possible ways B can occur through different scenarios
