Discussion Exercise 4 Spring 2009 Name Matthew Marck Section 0101 Probability A Empirical Probability I want the class to empirically determine the probability of selecting a piece of pasta and it being red from a large population of pasta There is a bag with a large number of dried pasta of different colors in it Yes the easiest way to determine P Red Pasta would be to dump out the pasta and count them all please don t Stick with the concept here and as a class decide what the best way to sample in such a way that you get a good sample I do not want you to use random numbers this time Come up with something else that should fit the assumptions of a good sample I was unable to attend discussion this week so instead of using the pasta sampling I used a change cup I have been collecting and chose to select dimes as my red pasta I also couldn t create an empirical probability 1 List here the main issues that were discussed and how you decided to conduct the study In order to best conduct the study a sample population must be randomly selected To do this I have randomly and unable to view the coins eyes closed selected 20 coins Then counted up the number of dimes in this sample population and recorded it 2 For an empirical study you need a lot of samples As a group decide how many samples that you will be taking Write the number here 20 coins Pass around the bag so that people can collect their samples Work on the problems listed below using theoretical probability while you wait your turn Since we are estimating the probability empirically we now need to generate a cumulative frequency histogram of the data This will be the responsibility of your TA so give that person your data Provide the number of pasta sampled and the number of those pieces of pasta that were red 3 What is the empirically calculated probability of sampling a red pasta piece for the class Since I was unable to attend discussion this week I only have my own data to go by so My calculated probability not empirical of the sampling was 6 20 coins P 0 3 or 30 4 After having done this exercise think back and decide what assumption of taking a good sample you most concerned might be violated Explain why you think it might be an issue in this sampling scheme 2pts Well the 4 aspects of a good sample are unbiased random entire population and independent I would have to say that independent would be the issue here By removing the pasta from the bag then counting we are shrinking the overall population for the next person in our group and even ourselves Also in my case bias may have been a factor because coins are not all the same size I tried to be as unbiased as possible in my selections 1 A bag contains 4 white balls 6 black balls 3 red balls and 8 green balls If one ball is drawn from the bag find the probability that it will be black 2 Now what is the probability of sampling 1 ball and it being either white or green B Theoretical Probability 6 21 0 29 100 29 P white 4 21 0 19 P green 3 21 0 14 0 19 0 14 0 33 100 33 3 What is the probability of drawing 1 ball finding it white replacing it in the bag and drawing a 2nd ball and finding it green P white P green 0 19 0 33 0 063 100 6 3 4 A couple wants 2 children If the probability of having a girl is 0 5 what is the probability that they will have at least 1 girl P 1 girl 1 boy 0 5 or P 2 girls 0 5 0 5 B G G B G G 3 0 25 25 5 Below is information on the Titanic s mortality data Survived Died Men Women 332 318 1360 104 Boys Girls 29 35 27 18 a If we randomly select 1 passenger who died what is the probability that it was a man 1360 1517 0 897 89 7 b What is the probability of selecting 1 person out of all the passengers on the boat and it being a boy that survived OR girl that survived 29 27 2223 0 025 100 2 5 6 For an experiment if you know the probability of Outcome A 0 6 and the probability of Outcome B 0 75 are these events mutually exclusive Why or why not They are not mutually exclusive because they have different probabilities of outcomes Mutually exclusive means each outcome shouldn t affect the next other outcome thus they would be the same probability