G: SAMPLING WITH AND WITHOUT REPLACEMENT H: SETS AND VENN DIAGRAMS CH 22GH.

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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