Week 3

Sections 2.3-2.4

**Product Rule:**If there are n_{1}possible choices for the first element of a set, n_{2}possible choices for the second element of a set, …., n_{k}possible choices for the k-th element of a set, then the number of possible sets is**(n**(Can use tree diagram to enumerate all the possibilities)_{1}n_{2}…n_{k}).

**Permutation 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)=P**. Using factorial notation, we have_{k,n}**P**_{k,n}= n!/(n-k)!_{.}**Combination 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