SECTION 8.5 PROBLEM SET: INDEPENDENT EVENTS
The distribution of the number of fiction and non-fiction books checked out at a city's main library and at a smaller branch on a given day is as follows.
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MAIN (M) |
BRANCH (B) |
TOTAL |
FICTION (F) |
300 |
100 |
400 |
NON-FICTION (N) |
150 |
50 |
200 |
TOTALS |
450 |
150 |
600 |
Use this table to determine the following probabilities:
- P(F)
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- P(M|F)
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- P(N|B)
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4. Is the fact that a person checks out a fiction book independent of the main library? Use probabilities to justify your conclusion. |
For a two-child family, let the events E, F, and G be as follows.
E: The family has at least one boy
F: The family has children of both sexes
G: The family's first born is a boy
- Find the following.
- P(E)
- P(F)
- P(E∩F)
- Are E and F independent? Use probabilities to justify your conclusion.
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- Find the following.
- P(F)
- P(G)
- P(F∩G)
- Are F and G independent? Use probabilities to justify your conclusion.
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Do the following problems involving independence.
- If P(E)=.6, P(F)=.2, and E and F are independent, find P(E and F).
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- If P(E)=.6, P(F)=.2, and E and F are independent, find P(E or F).
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- If P(E)=.9, P(F|E)=.36, and E and F are independent, find P(F).
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- If P(E)=.6, P(E or F) = .8, and E and F are independent, find P(F).
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- In a survey of 100 people, 40 were casual drinkers, and 60 did not drink. Of the ones who drank, 6 had minor headaches. Of the non-drinkers, 9 had minor headaches. Are the events "drinkers" and "had headaches" independent?
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- It is known that 80% of the people wear seat belts, and 5% of the people quit smoking last year. If 4% of the people who wear seat belts quit smoking, are the events, wearing a seat belt and quitting smoking, independent?
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- John's probability of passing statistics is 40%, and Linda's probability of passing the same course is 70%. If the two events are independent, find the following probabilities.
- P( both of them will pass statistics)
- P(at least one of them will pass statistics)
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- Jane is flying home for the Christmas holidays. She has to change planes twice. There is an 80% chance that she will make the first connection, and a 90% chance that she will make the second connection. If the two events are independent, find the probabilities:
- P( Jane will make both connections)
- P(Jane will make at least one connection)
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For a three-child family, let the events E, F, and G be as follows.
E: The family has at least one boy
F: The family has children of both sexes
G: The family's first born is a boy
- Find the following.
- P(E)
- P(F)
- P(E∩F)
- Are E and F independent?
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- Find the following.
- P(F)
- P(G)
- P(F∩G)
- Are F and G independent?
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SECTION 8.5 PROBLEM SET: INDEPENDENT EVENTS
- P(K|D)=0.7, P(D)=0.25 and P(K)=0.7
- Are events K and D independent? Use probabilities to justify your conclusion.
- Find P(K∩D)
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- P(R|S)=0.4, P(S)=0.2 and P(R)=0.3
- Are events R and S independent? Use probabilities to justify your conclusion.
- Find P(R∩S)
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- At a college:
54% of students are female
25% of students are majoring in engineering.
15% of female students are majoring in engineering.
Event E = student is majoring in engineering
Event F = student is female
- Are events E and F independent? Use probabilities to justify your conclusion.
- Find P(E∩F)
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- At a college:
54% of all students are female
60% of all students receive financial aid.
60% of female students receive financial aid.
Event A = student receives financial aid
Event F = student is female
- Are events A and F independent? Use probabilities to justify your conclusion.
- Find P(A∩F)
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