chapter 13: general rules of probability Flashcards
For any two events A and B
P(A or B) = P(A) + P(B) − P(A and B)
i.e. the A group’s percentage, plus the B groups percentage, minus the “both” group
Two events A and B are independent if…
knowing that one occurs does not change the probability that the other occurs. If A and B are independent,
P(A and B) = P(A)P(B)
i.e. both = the first times the second, probability-wise
disjointedness VS independence
Unlike disjointness, we cannot depict independence in a Venn diagram because it involves the probabilities of the events rather than just the outcomes that make up the events.
conditional probability
The probability we assign to an event can change if we know that some other event has occurred.
you can read the | (bar) in conditional probabilities as:
“given the information that…”
The idea of a conditional probability P(B | A) of one event B given that another event A occurs is
the proportion of all occurrences of A for which B also occurs.
How would you phrase these?
P(truck | imported)=0.546
P(imported | truck)=0.207
The first answers the question, “What proportion of imports are trucks?” The second answers, “What proportion of trucks are imports?”
Phrase this:
P (male | rich)
Probability of selecting a male given that I’m choosing one of the teens that chose “rich”
True or false: “70% of females are married.” is a conditional probability
True, because This is the chance of being married given the person is female, so it is conditional.
the key to success in applying probability ideas
is formulating a problem in the language of probability
to find the probability that ALL of several events occur.
The Multiplication rule for any two events is
The probability that both of two events A and B happen together can be found by
P(A and B) = P(A)P(B | A)
Here, P(B | A) is the conditional probability that B occurs, given the information that A occurs.
The probability of at least one [variable] can be found as
1 – P(the variable’s opposite)
