9
QuizMultiple Choice

Geometric Random Variables

Question 9 • Probability and Statistics with Applications Honors Sem-2-FL-1210300 (2024-2025)

A coin is flipped 25 times, and we would like to know the probability that 15 or more of those flips are heads side up.

Answer
A
Yes, the geometric distribution is appropriate.
B
No, since each trial is not independent of the other trials.
C
No, because it is not looking for the first occurrence of success.
D
No, since a success and failure on each trial cannot be defined..

Explanation

A geometric distribution models the number of trials needed to get the first success. Here, the 25 flips are a fixed number of trials, and we want the probability of getting at least 15 heads among them—not the waiting time until the first head. So the geometric distribution is not appropriate; choice C is correct.

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