SECTION 8.2 PROBLEM SET: MUTUALLY EXCLUSIVE EVENTS AND THE ADDITION RULE
Determine whether the following pair of events are mutually exclusive.
1) A = {A person earns more than $25,000}
B = {A person earns less than $20,000}
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2) A card is drawn from a deck.
C = {It is a King} D = {It is a heart}.
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3) A die is rolled.
E = {An even number shows}
F = {A number greater than 3 shows}
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4) Two dice are rolled.
G = {The sum of dice is 8}
H = {One die shows a 6}
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5) Three coins are tossed.
I = {Two heads come up}
J = {At least one tail comes up}
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6) A family has three children.
K = {First born is a boy}
L = {The family has children of both sexes}
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Use the Addition Rule to find the following probabilities.
7) A card is drawn from a deck. Events C and D are:
C = {It is a king}
D = {It is a heart}
Find P(C or D).
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8) A die is rolled. The events E and F are:
E = {An even number shows}
F = {A number greater than 3 shows}
Find P(E or F).
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9) Two dice are rolled. Events G and H are:
G = {The sum of dice is 8}
H ={Exactly one die shows a 6}
Find P(G or H).
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10) Three coins are tossed. Events I and J are:
I = {Two heads come up}
J = {At least one tail comes up}
Find P(I or J).
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11) At a college, 20% of the students take Finite Mathematics, 30% take Statistics and 10% take both. What percent of students take Finite Mathematics or Statistics? |
12) This quarter, there is a 50% chance that Jason will pass Accounting, a 60% chance that he will pass English, and 80% chance that he will pass at least one of these two courses. What is the probability that he will pass both Accounting and English? |
Questions 13 - 20 refer to the following: The table shows the distribution of Democratic and Republican U.S by gender in the 114th 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.
13) P(M and D) |
14) P(F and R) |
15) P(M or D) |
16) P(F or R) |
17) P(Mc or R) |
18) P(M or F) |
19) Are the events F, R mutually exclusive?
Use probabilities to support your conclusions.
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20) Are the events F, T mutually exclusive?
Use probabilities to support your conclusion.
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SECTION 8.2 PROBLEM SET: MUTUALLY EXCLUSIVE EVENTS AND THE ADDITION RULE
Use the Addition Rule to find the following probabilities.
21) If P(E) = .5 , P(F) = .4 , E and F are mutually exclusive, find P(E and F). |
22) If P(E) = .4 , P(F) = .2 , E and F are mutually exclusive, find P(E or F). |
23) If P(E) = .3, P(E or F) = .6 , P(E and F) = .2, find P(F). |
24) If P(E) = .4, P(F) = .5 , P(E or F) = .7, find P(E and F). |
25) In a box of assorted cookies, 36% of cookies contain chocolate and 12% of cookies contain nuts. 8% of cookies have both chocolats and nuts. Sean is allergic to chocolate and nuts. Find the probability that a cookie has chocolate chips or nuts (he can’t eat it). |
26) 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.
Find the probability that a course requires a final exam or a research paper.
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Questions 25 and 26 are adapted from Introductory Statistics from OpenStax under a creative Commons Attribution 3.0 Unported License, available for download free atcnx.org/content/col11562/latest u