Date: Tuesday, 23rd October 2001 19:57:04 (Central Daylight Time) From: Mark Jacobson To: Jimi.Hendrix@uni.edu Subject: Re: HW5 --------------------------------------------------------------------------- On Tue, 23 Oct 2001 Jimi.Hendrix@uni.edu wrote: > Mark~ > For the homework on Page 156-#6c and #8, I have the venn diagrams done, > but I'm not sure how to do probablities for those problems. > Also on Page 161 #20, I am really confused on how to do that problem > also. > Thank you! > ~Jimi --------------------------------------------------------------------------- Jimi, Take the following Ghostbuster's example: There are a total of 100 Ghostbuster's tools in the Universe. Peter Venkman uses 25 tools, Raymond Stantz uses 30 tools, Egon Spengler uses 35 tools. Pete and Ray share 10 tools, Pete and Egon share 13 tools, Ray and Egon share 15 tools. All three of the Ghosbusters share 6 tools. How many tools are in the collection of tools used by Pete and Ray and Egon? 58 tools 58 = 25 + 30 + 35 - 10 - 13 - 15 + 6 How many tools are never used by Pete, Ray or Egon? 100 - 58 = 42 tools are never used by Pete, Ray or Egon. The 42 tools might be used by Winston Seddemore, Jeannine, or by Louis Tully, perhaps. [ Note: Here is specific help for page 156, #6(c). ] If a Ghostbusters tool is selected at random, what is the probability it is used by exactly two of the Ghostbusters? How many tools are used by Pete and Ray, but not by Egon? 10 - 6 = 4 How many tools are used by Pete and Egon, but not by Ray? 13 - 6 = 7 How many tools are used by Ray and Egon, but not by Pete? 15 - 6 = 9 How many tools are used by exactly two of the Ghostbusters? 4 + 7 + 9 = 20 tools are used by exactly two of the three Ghostbusters. So what is the probability that a random tool chosen from the entire toolbox will be one used by exactly two? 20/100 = 1/5 = 0.2 is the probability. What is the probability that a random tool chosen from only the set of 58 tools that Pete and Ray and Egon use would be a tool used by exactly two of them? 20 ---- = 0.34 or about 34 percent chance it would be a tool only 58 used by two of the Ghostbusters. I hope this helps. ------------------------------------------------------------------------- > Also on Page 161 #20, I am really confused on how to do that problem The page 161 #20 problem involves three questions. Remember, in the sets counting problems there are THREE sets. The Pete Venkman tools, the Raymond Stantz tools and the Egon Spengler tools. P, R and E. Suppose you called the set of students who answered question #1 the P or Pete set. The set of students who answered question #2 could be called the R or Raymond set. The set of students who answered question #3 could be called the E or Egon set. Figuring out how many students of the 21 students answered exactly one question is like figuring out how many tools of the Ghosbusters 58 tools would be used by EXACTLY ONE Ghostbuster. A Venn diagram will help in this process. Mark On Tue, 23 Oct 2001 Jimi.Hendrix@uni.edu wrote: > Mark~ > For the homework on Page 156-#6c and #8, I have the venn diagrams done, > but I'm not sure how to do probablities for those problems. > Also on Page 161 #20, I am really confused on how to do that problem > also. > Thank you! > ~Jimi