Question 10 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)
A teacher claims that there is a 50% 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% probability claim.
Answer
A
Yes, the teacher should not collect homework assignments next week to bring the probability of homework being collected back to 0.5.
B
No, if the teacher collects homework five days in a row, it is not possible for the probability of homework being collected to be 0.5.
C
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.
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% chance means collecting and not collecting homework are equally likely on any given day; it does not guarantee a particular pattern over a short period. Collecting homework all five days does not make the teacher less likely to collect it the next week, and she does not need to skip assignments to balance the results. Thus, whether she collects homework on a particular day cannot be determined from the five-day streak.
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