Probability Flashcards
Is a numerical statement about the likelihood that an event will occur.
Probability
is the probability of an event occurring based on historical data and mathematical calculations
Objective probability
Ex. The probability of tossing a coin once and getting a head
is the probability of an event occurring based on personal judgment and experience
Subjective probability
Formula for Objective probability
P(event) = Number of occurrences of the event / Total number of outcomes
Ex. P (head) = Number of ways getting a head / Number of possible outcome (head or tail)
P (head) = 1 /2
Events are said to be ____ if only one event can occur on any one trial
Mutually exclusive
Events are said to be ____ if the list of outcomes includes every possible outcome
Collectively exhaustive
Adding Mutually Exclusive Events
P (A or B) = P(A) + P(B)
Ex. P (spade or club) = P(spade) + P(club)
= 13/52 + 13/52
= 26/52 = ½ = 0.5 = 50%
Law of Addition for events That Are Not Mutually Exclusive
P(A or B) = P(A) + P(B) – P(A and B)
Ex. P (five or diamond) = P(five) + (P(diamond) – P(five and diamond)
= 4/52 + 13/52 – 1/52
= 16/52 = 4/13
Events may either be
independent
dependent
the occurrence of one event has NO effect on the probability of occurrence of the second event.
Independent
the occurrence of one event has an effect on the probability of occurrence of the second event.
dependent
Is the probability of an event occurring given that another event has taken place.
Conditional Probability
Formula for Conditional probability
P(A | B) = P(AB) / P(B)
A = the event that we are interested in
B = the event that has already occurred
Is the product of marginal probabilities
Joint Probability
Formula for Joint probability
P(AB) = P(A I B) P(B)
