6.2E: Exercises - Mutually Exclusive Events and the Addition Rule
PROBLEM SET: MUTUALLY EXCLUSIVE EVENTS AND THE ADDITION RULE
Determine whether the following pair of events are mutually exclusive.
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1) A = {A person earns more than $25,000} B = {A person earns less than $20,000} |
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} |
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} |
6) A family has three children. K = {First born is a boy} L = {The family has children of both sexes} |
Use the Addition Rule to find the following probabilities.
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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 \(\cup\) D). |
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 \(\cup\) 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 \(\cup\) H). |
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 \(\cup\) J). |
| 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 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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13) P(M \(\cap\) D) |
14) P(F \(\cap\) R) |
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15) P(M \(\cup\) D) |
16) P(F \(\cup\) R) |
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17) P(M \(\cup\) R) |
18) P(M \(\cup\) F) |
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19) Are the events F, R mutually exclusive?
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20) Are the events F, T mutually exclusive?
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Use the Addition Rule to find the following probabilities.
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21) If P(E) = .5 , P(F) = .4 , E and F are mutually exclusive, find P(E \(\cap\) F). |
22) If P(E) = .4 , P(F) = .2 , E and F are mutually exclusive, find P(E \(\cup\) F). |
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23) If P(E) = .3, P(E \(\cup\) F) = .6 , P(E \(\cap\) F) = .2, find P(F). |
24) If P(E) = .4, P(F) = .5 , P(E \(\cup\) F) = .7, find P(E \(\cap\) F). |
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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.
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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 athttp://cnx.org/content/col11562/latest u