In a basketball arena, Quiz
The question sheet
Reveal any answer as you study-
What percent of the fans are rooting for the home team?
- 20%
- 67%
- 25%
- 70%
Reveal answer
Answer: 70%
Source evidence
PDF page 152: • 70% of the fans are rooting for the home team.
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What percent of the fans are wearing blue?
- 25%
- 70%
- 67%
- 20%
Reveal answer
Answer: 25%
Source evidence
PDF page 152: • 25% of the fans are wearing blue.
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What percent of fans are wearing blue and rooting for the away team?
- 20%
- 25%
- 67%
- 70%
Reveal answer
Answer: 20%
Source evidence
PDF page 152: • 20% of the fans are wearing blue and are rooting for the away team.
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In the arena problem, what does event A represent?
- A fan roots for the away team
- A fan roots for the home team
- A fan is wearing blue
- A fan is wearing red
Reveal answer
Answer: A fan roots for the away team
Source evidence
PDF page 152: Let A be the event that a fan is rooting for the away team. Let B be the event that a fan is wearing blue.
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In the college class example, what percent of students are female?
- 45%
- 75%
- 50%
- 60%
Reveal answer
Answer: 60%
Source evidence
PDF page 153: In a particular college class, 60% of the students are female. Fifty percent of all students in the class have long hair. Forty-five percent of the students are female and have long hair. Of the female students, 75% have long hair. Let F be the event that a student is female. Let L be the event that a student has long hair. One student is picked randomly. Are the events of being female and having long hair independent?
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In the college class example, what percent of all students have long hair?
- 45%
- 50%
- 75%
- 60%
Reveal answer
Answer: 50%
Source evidence
PDF page 153: In a particular college class, 60% of the students are female. Fifty percent of all students in the class have long hair. Forty-five percent of the students are female and have long hair. Of the female students, 75% have long hair. Let F be the event that a student is female. Let L be the event that a student has long hair. One student is picked randomly. Are the events of being female and having long hair independent?
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In the college class example, what does event F represent?
- A student is male
- A student has long hair
- A student is female
- A student is picked
Reveal answer
Answer: A student is female
Source evidence
PDF page 153: In a particular college class, 60% of the students are female. Fifty percent of all students in the class have long hair. Forty-five percent of the students are female and have long hair. Of the female students, 75% have long hair. Let F be the event that a student is female. Let L be the event that a student has long hair. One student is picked randomly. Are the events of being female and having long hair independent?
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What are the given values of P(F) and P(L)?
- P(F)=0.50; P(L)=0.60
- P(F)=0.45; P(L)=0.75
- P(F)=0.75; P(L)=0.45
- P(F)=0.60; P(L)=0.50
Reveal answer
Answer: P(F)=0.60; P(L)=0.50
Source evidence
PDF page 153: • P(F)=0.60; P(L)=0.50
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Why can't the second condition be used in the college class example?
- P(L) is unknown
- P(F) is unknown
- P(F ∩ L) is unknown
- P(F|L) is not yet known
Reveal answer
Answer: P(F|L) is not yet known
Source evidence
PDF page 153: NOTE The choice you make depends on the information you have. You could use the first or last condition on the list for this example. You do not know P(F|L) yet, so you cannot use the second condition.
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What is the value of P(F)P(L) computed in the example?
- 0.30
- 0.75
- 0.50
- 0.45
Reveal answer
Answer: 0.30
Source evidence
PDF page 153: Solution 1 P(F ∩ L) = P(F)P(L) . We are given that P(F ∩ L) = 0.45 , but Check whether P(F)P(L) = (0.60)(0.50) = 0.30 . The events of being female and having long hair are not independent because P(F ∩ L) does not equal P(F)P(L) . Solution 2 Check whether P(L|F) equals P(L) . We are given that P(L|F) = 0.75 , but P(L) = 0.50 ; they are not equal. The events of being female and having long hair are not independent. Interpretation of Results The events of being female and having long hair are not independent; knowing that a student is female changes the probability that a student has long hair.
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What does knowing a student is female do to the probability of long hair?
- Makes it certain
- Leaves it unchanged
- Makes it zero
- Changes the probability
Reveal answer
Answer: Changes the probability
Source evidence
PDF page 153: Solution 1 P(F ∩ L) = P(F)P(L) . We are given that P(F ∩ L) = 0.45 , but Check whether P(F)P(L) = (0.60)(0.50) = 0.30 . The events of being female and having long hair are not independent because P(F ∩ L) does not equal P(F)P(L) . Solution 2 Check whether P(L|F) equals P(L) . We are given that P(L|F) = 0.75 , but P(L) = 0.50 ; they are not equal. The events of being female and having long hair are not independent. Interpretation of Results The events of being female and having long hair are not independent; knowing that a student is female changes the probability that a student has long hair.
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In the arena problem, what percent of fans are wearing blue?
- 70%
- 67%
- 20%
- 25%
Reveal answer
Answer: 25%
Source evidence
PDF page 152: • 25% of the fans are wearing blue.
Introductory Business Statistics
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