Probability Rules Part 2

Contingency Tables

• Translate percentages to probabilities to fill in the table ( total= 100%/1)

• Because the cells of the table show disjoint events, the probabilities always add to the margins totals across the rows or down columns

• Entries should always match up with corresponding venn diagram

Which is better: contingency table or venn diagram?

All depends on the questions asked and personal preference

Drawing without Replacement

taking something out of the sample space and it’s no longer available → changes # of total sample size and # of that outcome to occur

General Multiplication Rule Formula

P(A∩B)= P(A)*P(B|A)

Tree Diagrams

a type of picture that organize and shows sequences of events (important for conditional probability)

What can go wrong?

• Dont use simple probability when the general rule is appropriate

• Don’t assume that outcomes are disjoint without checking that they are

• Remember the general rules always applies when the outcomes are independent or disjoint

• Dont find probabilities for samples drawn without replacement as if they’ve been drawn with replacement

• Dont reverse conditioning naively

• The true probability may be counterintuitive

• Dont confuse disjoint and independent

• What rule to use is all based on wording