Statistics Proability Assignment

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Delaware State University *

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201

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Statistics

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Apr 25, 2024

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docx

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Uploaded by MegaComputerPelican38

Part A: Events and Sample Space 1 . In a group of adults, some have iPods, and others do not. Two adults are randomly selected from this group: (4 points) a) How many total outcomes are possible? iPod and iPod, iPod and no iPod, No iPod and No iPod, No iPod and iPod b) Draw a tree diagram for this experiment. 2. Using the information from the question, list all the outcomes included in each of the following events. Indicate which are simple and which are compound events. (8 points) a. One person has an iPod, and the other does not. IN, NI - Compound b. At least one person has an iPod. II, IN, NI - Simple c. Not more than one person has an iPod. IN, NI, NN - Simple d. The first person has an iPod and the second does not. II, IN - Compound Part B: Contingency Tables and Probabilities

A sample of 135 adults was taken from a senior community in Wisconsin. Each person was asked to list their political affiliation. Their answers were put into a contingency table. Use the following contingency table to answer the following questions. (12 points) democrat republican independent Total male 25 30 15 70 female 40 20 5 65 65 50 20 135 1. What is the probability that a person selected at random will be a male? 70/135 = 51.85% 2. What is the probability that a person selected at random will be a republican and a female? P(A n B) = P(A) * P(B|A) = 50/135 * 20/50 = 14.8% 3. Find the probability that a person selected at random will be a male or a democrat. P(A u B) = P(A) + P(B) - P(A n B) = 70/135 + 65/135 - 25/135 = 110/135 = 81.48% 4. Calculate the probability that a person selected at random will be an independent given that the person is a female. = 5/65 = 7.69% 5. Are the event democrat and the event republican mutually exclusive or non-mutually exclusive events? You must show the proof of your answer to receive any points. P(Democrat and Republican) = 0 There is no overlap in the data; one can not be both democrat and republican. 6. Are the event republican and the event male Independent events? You must show the proof of your answer to receive any points. P(republican) = 50/135 = 0.37 P(male) = 70/135 = 0.52 P(republican | male) = 30/70 = 0.43 P(male | republican) = 30/50 = 0.6 The probability of republican given male does not match the probability of republican. Additionally, the probability of male given the probability of republican does not match the probability of male. Therefore, these events are mutually exclusive.

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