G: SAMPLING WITH AND WITHOUT REPLACEMENT H: SETS AND VENN DIAGRAMS CH 22GH
G: Sampling with and without replacement Sampling Sampling with replacement Sampling without replacement
Industrial Sampling Sampling is commonly used in the quality control of industrial processes. How it’s made Example of quality control in the work force.
Consider a box containing 3 red, 2 blue and 1 yellow marble. If we sample two marbles, what is the probability we select BR? With replacement Without replacement
MORE! A box contains 3 red, 2 blue, 1 yellow marble. Find the probability of getting two different colours: If replacement occurs. If replacement does not occur.
MORE! A box contains 3 red, 2 blue, 1 yellow marble. Find the probability of getting two different colours: If replacement occurs. If replacement does not occur.
Even More! A bag contains 5 red and 3 blue marbles. Two marbles are drawn simultaneously from the bag. Determine the probability that at least one is red.
Sets and Venn Diagrams Venn Diagrams – way to represent data from a sample space. Rectangle – complete sample space U. Circles – particular events
Example Roll a 6-sided die. What is the sample space U? U = {1, 2, 3, 4, 5, 6}. U is a set. If the event A is “a number less than 3”, then how many outcomes are there? A = {1, 2} The Venn diagram below illustrates the event A within the universal set U. n(U) = 6 and n(A) = 2, so
Set Notation Universal set or sample space U Complement A’ If U = {1, 2, 3, 4, 5, 6} and A = {2, 4, 6}, then A’ = {1, 3, 5}
Set Notation denotes the intersection of sets A and B. This sets contains all the elements common to both sets. denotes the union of sets A and B. This set contains all the elements belonging to A or B or both A and B.
Disjoint Sets Disjoint sets are sets which do not have elements in common.
Example Let A be the set of all factors of 6, B be the set of all positive even integers < 11, and
Answer Let A be the set of all factors of 6, B be the set of all positive even integers < 11, and
Another superb example
Another superb answer
Almost finished – just a few more In a class of 30 students, 19 study Physics, 17 study Chemistry, and 15 study both of these subjects. Display this info on a Venn Diagram and determine the probability that a randomly selected class member studies: a) Both subjects b) At least one of the subjects c) Physics but not Chemistry d) Exactly one of the subjects e) Neither subject
Answer In a class of 30 students, 19 study Physics, 17 study Chemistry, and 15 study both of these subjects. Display this info on a Venn Diagram and determine the probability that a randomly selected class member studies:
Use a Venn diagram to