Two-Way Tables and Probability
Task
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Each student in a random sample of seniors at a local high school participated in a survey. These students were asked to indicate their gender and their eye color. The following table summarizes the results of the survey.
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 |
Eye color |
||||
Brown |
Blue |
Green |
Total |
||
Gender |
Male |
50 |
40 |
20 |
110 |
Female |
40 |
40 |
10 |
90 |
|
Total |
90 |
80 |
30 |
200 |
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Suppose that one of these seniors is randomly selected. What is the probability that the selected student is a male?
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Suppose that one of these seniors is randomly selected. What is the probability that the selected student has blue eyes?
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Suppose that one of these seniors is randomly selected. What is the probability that the selected student is a male and has blue eyes?
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Suppose that one of these seniors is randomly selected. What is the probability that the selected student is a male or has blue eyes?
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Suppose that one of these seniors is randomly selected. What is the probability that the selected student has blue eyes, given that the student is male?
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Suppose that one of these seniors is randomly selected. What is the probability that the selected student is a male, given that the student has blue eyes?
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IM Commentary
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The purpose of this task is to provide practice using data in a two-way table to calculate probabilities, including conditional probabilities (S.CP.4). This task provides a good starting point for a discussion of conditional probabilities leading to the concept of independence. In particular, focus on the difference between the two conditional probabilities calculated in parts (e) and (f).
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Solution
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a. \({number \ of \ males \over number \ of \ students}={110 \over 200}=0.55\)
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    b. \({number \ of \ students \ with \ blue \ eyes \over number \ of \ students}={80 \over 200}=0.40\)
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    c. \({number \ of \ males \ with \ blue \ eyes\over number \ of \ students}={40 \over 200}=0.20\)
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    d. \({number \ of \ males \ + \ number \ of \ blue \ eyed \ females\over number \ of \ students}={110 \ + \ 40 \over 200}=0.75\)
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        OR
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        \({number \ of \ males \ + \ number \ of \ blue \ eyed \ students \ - \ number \ of \ blue \ eyed \ boys \over number \ of \ students}={110 \ + \ 80 \ - \ 40 \over 200}=0.75\)
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    e. \({number \ of \ blue \ eyed \ males \over number \ of \ males}={40 \over 110}=0.36\)
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     f. \({number \ of \ blue \ eyed \ males \over number \ of \ blue \ eyed \ students}={40 \over 80}=0.50\)
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Two-Way Tables and Probability
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Each student in a random sample of seniors at a local high school participated in a survey. These students were asked to indicate their gender and their eye color. The following table summarizes the results of the survey.
Â
 |
Eye color |
||||
Brown |
Blue |
Green |
Total |
||
Gender |
Male |
50 |
40 |
20 |
110 |
Female |
40 |
40 |
10 |
90 |
|
Total |
90 |
80 |
30 |
200 |
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-
Suppose that one of these seniors is randomly selected. What is the probability that the selected student is a male?
 -
Suppose that one of these seniors is randomly selected. What is the probability that the selected student has blue eyes?
 -
Suppose that one of these seniors is randomly selected. What is the probability that the selected student is a male and has blue eyes?
 -
Suppose that one of these seniors is randomly selected. What is the probability that the selected student is a male or has blue eyes?
 -
Suppose that one of these seniors is randomly selected. What is the probability that the selected student has blue eyes, given that the student is male?
 -
Suppose that one of these seniors is randomly selected. What is the probability that the selected student is a male, given that the student has blue eyes?
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