Probability Flashcards
What is the probability formula?
Probability of event x = # of outcomes in which x occurs / total # of outcomes in the experiment
What is the probability of a sample space?
1
What is the probability rule for 2 independent events?
P(A and B) = P(A) x P(B)
What is the shortcut to calculate the probability when an event has more than one possible outcome?
Number of outcomes producing the event * probability of one outcome
This shortcut can be used only when each of the outcomes has the same probability
What is the formula for calculating the probability of multiple outcomes with “at least”?
First calculate the probabilities of the mutually exclusive scenarios, then add the probabilities to determine the final probability.
What is the formula for dependent events?
P(A and B) = P(A) x P(B|A)
P(B|A) = the probability that B will occur given that A has already occurred
What are mutually exclusive events?
Events that cannot occur at the same time
What is the addition rule for mutually exclusive events?
P(A or B) = P(A) + P(B)
Steps for at least probability problems:
- Define the mutually exclusive scenarios
- Calculate the probability of each scenario
- Add the probabilities together
When the question asks for the probability that “at least one” outcome will occur, what formula can you consider using to simplify the problem?
Complementary events:
P(at least 1 outcome occurs) = 1 - P(none of these outcomes occur)
What is the probability that some number of items will be selected?
Number of ways that some number of items must be selected / total # of ways that the items can be selected
When asked the probability that some number of items will NOT be selected, what formula can you use?
Number of ways that some number of items must not be selected / # of ways that all items can be selected.
