A teacher claims that there is a 50 percent chance that she will collect homework for a grade on any given day. One week, she collected all five daily homework assignments. A student in this class is upset and explains that the teacher should not collect any homework assignments the following week in order to honor her 50 percent probability claim. Is the student’s reasoning correct?
Answer
A
Yes, the teacher should not collect homework assignments next week to bring the probability of homework being collected back to 0 point 5 .
B
Yes, it is unlikely that the teacher would randomly collect homework assignments five days in a row, so not having a homework collection next week is due to happen.
C
No, if the teacher collects homework five days in a row, it is not possible for the probability of homework being collected to be 0 point 5 .
D
No, collecting homework and not collecting homework are equally likely in the long run, so whether or not the teacher collects homework on any single day cannot be determined.
Explanation
A 50 percent chance on any given day means collecting and not collecting are equally likely for that day; it does not require the teacher to collect homework exactly half the days in each week. Collecting homework all five days last week does not make it due to be skipped next week. Whether homework is collected on a particular future day cannot be determined from last week’s results, so the best choice is “No, collecting homework and not collecting homework are equally likely in the long run.”
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