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A college student contacts classmates at random, one at a time, until one confirms living within five miles, with 55% of students living that close. Why is this classified as a geometric problem rather than binomial?
AThe probability of success changes with every contact made
BEach contact has more than two possible outcomes
CThe contacts are sampled from two separate groups
DThere is no fixed number of trials, only failures until one success
Answer & Solution
Correct answer: D. There is no fixed number of trials, only failures until one success
1. A binomial experiment requires a fixed, predetermined number of trials, n.
2. Here the number of students contacted is not fixed; you keep asking until you get a yes, which could happen on any contact.
3. Also, the success probability of 55% stays the same on every contact, satisfying the geometric conditions instead.
4. Option A contradicts the constant probability assumption, and options C and D describe conditions not present in this scenario.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.4 Geometric Distribution_
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