5
QuizMultiple Choice

Introduction to Probability — Quiz

Question 5 • Algebra II

Dropping a piece of buttered toast will theoretically land butter-side down with a probability of 0 point 6 5 Some students decided to test this theory and dropped five pieces of buttered toast. All five landed butter-side down. One of the students claims that the next piece of buttered toast dropped will land butter-side up because it is due to happen. Is the student’s reasoning correct?

Answer
A
No, if buttered toast lands butter-side down five times in a row, the probability must be higher than 0 point 6 5 .
B
No, the probability of buttered toast landing butter-side down is 0 point 6 5 over a large number of trials.
C
Yes, it is unlikely that five pieces of dropped buttered toast will land butter-side down, so butter up must be due.
D
Yes, the students need to start dropping buttered toast to land butter up to get back to 0 point 6 5 .

Explanation

The probability of landing butter-side down is 0.65 on each drop; previous drops do not make the next result “due” to be butter-side up. Over many trials, the proportion landing butter-side down is expected to be close to 0.65, but a streak of five does not change the probability of the next drop. So the student’s reasoning is incorrect, and choice B gives the relevant long-run probability.

AI-written and checked against the verified answer.

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