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Someone throws darts at a bullseye repeatedly until the first hit, which is described as failure, failure, failure, failure, failure, success, STOP. What does X represent in this geometric setup?
AThe number of throws until the first hit
BThe total number of throws in the session
CThe probability of hitting on any one throw
DThe number of hits recorded overall
Answer & Solution
Correct answer: A. The number of throws until the first hit
1. In a geometric experiment, the process repeats failures until it hits a single success, then stops.
2. The random variable X counts how many trials, including the final successful one, it took to get there.
3. In this dart example, X is the number of throws needed to hit the bullseye for the first time.
4. Options C and D describe a probability and a hit count rather than a trial count, so neither matches how X is defined.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.4 Geometric Distribution_
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