QR Project #3 Congress Version B CW

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Eastern Gateway Community College *

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105

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Statistics

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Feb 20, 2024

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Project # 3 – Congress(B) HOUSE OF REPRESENTATIVES Political Party Republican Democrat Independent Total Male 170 192 0 362 Female 23 57 0 80 Total 193 249 0 442 SENATE Political Party Republican Democrat Independent Total Male 38 50 1 89 Female 11 24 1 36 Total 49 74 2 125 COMBINED TABLE – CONGRESS - COMBINING HOUSE OF REPRESENTATIVES AND SENATE Political Party Republican Democrat Independent Total Male 208 242 1 451 Female 34 81 1 116 Total 242 323 2 567 These charts are for exercise purposes only. It does not depict the actual numbers represented in the US Government today. Must show calculations/formula for credit. Any answer given with no calculations shown will result in no credit for that answer. Please answer the questions below and show your work where applicable. All answers should be proportions rounded to the nearest thousandths (3 decimals) . For Example: this is what is required to be

shown if I ask this question – shown is how you are expected to answer: (please note that this is the correct formula and process whenever an or question is asked) Find the probability that a Senate is a Male or a Democrat: 89/125 + 74/125 – 50/125 = 113/125 = .904 • Find the probability that a randomly selected House of Representative is a male. Looking at the table provided, we can see that there are 362 male representatives out of a total of 442 representatives. Therefore, the probability of randomly selecting a male representative is: P(Male) = Number of male representatives / Total number of representatives = 362 / 442 To express this probability as a decimal, we can divide the numerator by the denominator: P(Male) ≈ .819 So, the probability that a randomly selected House of Representative is male is approximately .819 or 81.9% • Find the probability that a randomly selected Senator is a female. From the table provided, we can see that there are 36 female senators out of a total of 125 senators. Therefore, the probability of randomly selecting a female senator is: P(Female) = Number of female senators / Total number of senators = 36 / 125 To express this probability as a decimal, we can divide the numerator by the denominator: P(Female) ≈ .288 So, the probability that a randomly selected Senator is female is approximately .288 or 28.8%. • A House of Representative member is selected at random. Find the probability of each event: • The representative is a female The number of female representatives is 80 out of a total of 442 representatives. P(Female) = Number of female representatives / Total number of representatives = 80 / 442 P(Female) ≈ 0.181 The probability that a randomly selected representative is female is approximately .181 or 18.1% • The representative is an independent.

According to the table, there are 0 independent representatives out of a total of 442 representatives. P(Independent) = Number of independent representatives / Total number of representatives = 0 / 442 P(Independent) = 0 The probability that a randomly selected representative is an independent is 0%. • The representative is a female given that the representative is a Democrat The number of female Democrat representatives is 57 out of a total of 249 Democrat representatives. P(Female | Democrat) = Number of female Democrat representatives / Total number of Democrat representatives = 57 / 249 P(Female | Democrat) ≈ .229 The probability that a randomly selected representative is a female given that they are a Democrat is approximately .229 or 22.9%. • The representative is female and a Democrat The number of female Democrat representatives is 57 out of a total of 442 representatives. 3 P(Female and Democrat) = Number of female Democrat representatives / Total number of representatives = 57 / 442 P(Female and Democrat) ≈ 0.129 The probability that a randomly selected representative is both female and a Democrat is approximately .129 or 12.9% • A Senator is selected at random. Find the probability of each event • The senator is a female There are a total of 125 senators, and 36 of them are female. The probability that a randomly selected senator is female is 36/125 = .288. • The senator is not a Republican There are 49 Republicans among 125 senators. Thus, the number of senators who are not Republicans is 125 - 49 = 76. Therefore, the probability that a randomly selected senator is not a Republican is 76/125 = .608. • The senator is female or a Democrat There are 36 females and 74 Democrats among 125 senators. However, because there are female Democrats, they have been counted twice (once for being female and once for being a Democrat). There are 24 female Democrats. So, we need to subtract these from our total. The number of senators who are either female or a Democrat is 36 + 74 - 24 = 86. Thus, the probability that a randomly selected senator

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is female, or a Democrat is 86/125 = .688. • The senator is a male or a Democrat same as the previous question, there are 89 males and 74 Democrats among 125 senators. There are 50 male Democrats, so we need to subtract these from our total. The number of senators who are either male or a Democrat is 89 + 74 - 50 = 113. Therefore, the probability that a randomly selected senator is male, or a Democrat is 113/125 = .904. • Using the same row and column headings, create a combined table for the Congress (template created for you above – you can just fill in the table I already created) • A member of Congress is selected at random. Use the combined table to find the probability of each event. • The member is Independent There are a total of 567 members of Congress, and 2 of them are Independent. The probability that a randomly selected member is Independent is 2/567 = .0035. • The member is female and a Democrat There are 81 female Democrats among 567 members of Congress. Therefore, the probability that a randomly selected member is a female Democrat is 81/567 = .1428. • The member is male or a Democrat There are 451 males and 323 Democrats among 567 members of Congress. However, because there are male Democrats, they have been counted twice (once for being male and once for being a Democrat). There are 242 male Democrats. So, we need to subtract these from our total. The number of members who are either male or a Democrat is 451 + 323 - 242 = 532. Therefore, the probability that a randomly selected member is male, or a Democrat is 532/567 = .9383