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10_week_5_S3_W6_S1_Chapter_15_-_Probability_Rule_

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1 Statistics 10/Week 5 Session Three and Week six Session one (Chapter 15/Probability Rules) Professor Esfandiari The objective of this lecture is to discuss: The probability of an event General addition rule (overlapping and non-overlapping events), Conditional probability and link to contingency tables Multiplication rule applied to events that are independent General multiplication rule applied to compound events that does not require for the events to be independent Tree diagrams In the following table, you are given the information regarding gender and major of the students enrolled in an introductory statistics class. I collected this information from a statistics class (sample of convenience) and I am going to use this data to introduce you to the concepts described above. Table 1: frequency of gender by major Student # gender major Student # gender Major 1 2 1 20 2 1 2 2 3 21 2 1 3 2 1 22 1 1 4 2 1 23 1 3 5 2 1 24 1 2 6 1 2 25 2 1 7 2 1 26 1 2 8 2 2 27 1 1 9 1 2 28 1 1 10 1 3 29 2 1 11 2 3 30 1 2 12 1 1 31 1 2 13 2 1 32 2 1 14 2 3 33 1 1 15 2 1 34 1 3 16 1 1 35 1 1 17 2 2 36 1 2 18 2 3 37 2 3 19 1 2 38 2 2 39 1 1 Gender (1 = female, 2 = male) Major (1 = science related, 2 = social science related, 3 = undeclared)

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2 Table 2: Breakdown of the students by gender Table 3: The breakdown of the students in you class by major Table 4: Cross tabulation of the students by major and gender (contingency table)
3 Question one : If you pick a student at random, what is the probability that the person is male, female, science major, non-science major, undeclared? P (male) = 20/39 = 0.51 P (female) = 19/39 = 0.49 P (science major) = 20/39 = 0.51 P (social science major) = 11/39 = 0.28 P (undeclared) = 8/39 = 0.21 These probabilities are given in the form of percentages given in tables 1 and 2. Question 2 : Suppose that you pick and individual at random, given that she is a female, what is the probability that she will be a science major? Conditional probability : Remember from prior lectures, we talked about contingency tables we also discussed conditional distributions as restricting ourselves to a smaller group of individuals. So, if we only want to consider gender, we will have two conditional distributions one for males and one for females, that is distribution of males in different majors and distribution of females in different majors; you could generate two different bar charts one for males and one for females. If you only want to consider major then you could do three different bar charts for the three different majors with the percentage of male and female within each major. Conditional probability : When you only look at females, you are placing a condition on the events you are considering and you are interested in events such as: If you pick a person at random, given that she is a female, what is the probability that she will be a science major?

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