Stat 2000: Extra Help for Probability

Published: Tue, 10/30/12


 
I have some extra help for the probability stuff you are doing in class coming up, but first a couple of announcements.
Please note that my final exam prep seminar for Stat 2000 will be on Sunday, Dec. 2, in room 100 St. Paul's College, from 9 am to 9 pm .  For complete info about the seminar, and to register if you have not done so already, click this link:
Stat 2000 Seminar 
 
I am also offering seminars in Calculus, Linear Algebra, and Stat 1000 in the coming weeks.  You can get info about those seminars here:
Grant's One-Day Exam Prep Seminars
 
If you ever want to look back over a previous tip I have sent, do note that all my tips can be found in my archive.  Click this link to go straight to my archive: 
Grant's Homework Help Archive
 
Extra Tips for Probability
 
I am surprised to see a lot of probability questions on this assignment that are from Stat 1000, so I have attached a handout from my Basic Stats 1 study book with a more thorough discussion of making two-way tables and Venn diagrams.  Those of you who have my Basic Stats 1 book, should study Lesson 5: Introduction to Probability.
Excerpts from Grant's Probability Lesson in Basic Stats 1 
 
Conditional Probability
 
Here is another handout explaining the approach to determine a conditional probability:
Conditional Probability Handout
 
Essentially, in conditional probability, when it says "given A" is telling you that we know for sure that event A has occurred, so we are now only interested in outcomes that belong to A.  That becomes the "whole".  P(B|A) wants the fraction of that "whole" that also belongs to B.
 
For example, if you look at my question 18 in the probability handout above, I could add a part (d) that asks, "What is the probability someone is a basketball fan if they are a hockey fan?"  Any probability question that asks, what is the probability of B if event A has occurred, you are doing conditional probability. 
 
We want P(B|H).  I first look through my Venn diagram and find all the bits that belong to H, since we know for sure the person is a hockey fan. There are four bits in the H circle so I add those bits up: 33 + 31 + 8 + 5 = 77%.  Now, I gather all the bits in that H circle that represent people who are also basketball fans.  There are two bits: 8 + 5 = 13%.  Thus, the probability a person is a basketball fan if they are a hockey fan is 13%/77% or .13/.77 = .1688.
 
Here is a couple of extra conditional probability questions I have added to question 4 in my probability handout above:
Question 4 (g) and (h)
 
Here is a couple of extra conditional probability questions I have added to question 16 in my probability handout above: