6.4E: Exercises - Conditional Probability
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.
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MALE(M) |
FEMALE(F) |
TOTAL |
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DEMOCRATS (D) |
30 |
14 |
44 |
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REPUBLICANS(R) |
48 |
6 |
54 |
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OTHER (T) |
2 |
0 |
2 |
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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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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 |
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25-44 (R) |
95 |
228 |
143 |
81 |
188 |
61 |
796 |
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45-64 (S) |
83 |
256 |
136 |
80 |
150 |
67 |
772 |
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65+ (T) |
96 |
191 |
84 |
36 |
80 |
41 |
528 |
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Total |
274 |
675 |
363 |
197 |
418 |
169 |
2096 |
Use this table to determine the following probabilities:
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