7.4.1: Conditional Probability (Exercises)
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SECTION 8.4 PROBLEM SET: CONDITIONAL PROBABILITY
Questions 1 - 4: Do these problems using the conditional probability formula: \(P(A | B)=\frac{P(A \cap B)}{P(B)}\).
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Questions 5 - 8 refer to the following: The table shows the distribution of Democratic and Republican U.S. Senators by gender in the 114 th Congress as of January 2015.
| MALE(M) | FEMALE(F) | TOTAL | |
| DEMOCRATS (D) | 30 | 14 | 44 |
| REPUBLICANS(R) | 48 | 6 | 54 |
| OTHER (T) | 2 | 0 | 2 |
| TOTALS | 80 | 20 | 100 |
Use this table to determine the following probabilities:
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Do the following conditional probability problems.
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At a college, 72% of courses have final exams and 46% of courses require research papers. 32% of courses have both a research paper and a final exam. Let \(F\) be the event that a course has a final exam and \(R\) be the event that a course requires a research paper.
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SECTION 8.4 PROBLEM SET: CONDITIONAL PROBABILITY
Consider a family of three children. Find the following probabilities.
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Questions 21 - 26 refer to the following:
The table shows highest attained educational status for a sample of US residents age 25 or over:
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(D) Did not Complete High School |
(H) High School Graduate |
(C) Some College |
(A) Associate Degree |
(B) Bachelor Degree |
(G) Graduate Degree |
TOTAL | |
| 25-44 (R) | 95 | 228 | 143 | 81 | 188 | 61 | 796 |
| 45-64 (S) | 83 | 256 | 136 | 80 | 150 | 67 | 772 |
| 65+ (T) | 96 | 191 | 84 | 36 | 80 | 41 | 528 |
| Total | 274 | 675 | 363 | 197 | 418 | 169 | 2096 |
Use this table to determine the following probabilities:
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