Discrete Probability Distributions

Annotations:

• Historical sales record that 40 percent of all customers who enter store make a purchase. What is the probability that two of the next three customers will make a purchase?

1. how we know it's binomial
   1. 1) identical trials
   2. 2) TWO outcomes are possible in each trial
   3. 3) probability stays constant
   4. 4) all trial outcomes are independent
2. Sample Outcome Space

   Annotations:

   • SSS    SSF SFS FSS FFS FSF SFF FFF
   1. We know there are 8
3. Note
   1. 1

      Annotations:

      • the 3 in this expression is the number of sample space out comes (ssf, sfs, and fss) that correspond to the EVENT "two of the next three customers make purchases.
   2. 2

      Annotations:

      • .4 = p .6= q  is the probability that the customer does not make a purchase
4. Calculation

Annotations:

• (p)= success (f) = failure

1. not mutually Exclusive
2. Mutually Exclusive

Annotations:

• If A is the event... A Compliment is the event in which it will NOT occur.