Counting Rules for Enumerating All Possible Event Outcomes
- Product Rule:
If there are n1 possible choices
for the first element of a set, n2 possible choices for the second element of a
., nk possible choices for the k-th element of a set, then the
number of possible sets is (n1n2
nk). (Can use tree diagram to enumerate all the
Rule: When choosing k objects from a set
of n distinct objects to form an ordered sequence of size k, the number of possible
sets is n(n-1)
(n-k+1)=Pk,n. Using factorial
notation, we have Pk,n= n!/(n-k)!.
Rule: When choosing k objects from a set of n distinct objects, the number of possible
unordered subsets of size k is
Ck,n= n!/[k!(n-k)!] = Pk,n/k!.
How does the knowledge
of the occurrence of one event (B) affect probability assignment to another event (A)?
Given that event B occurs, the original sample space is reduced.
Thus the conditional probability of A, given that B occurs,
is defined as
P(A | B) = P( A
Note: From the definition of Conditional Probability,
we can get the Multiplication Rule: P( A
B) = P(A | B)P(B)