Successive trials within a binomial distribution are:__________________?
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Answer: B. Independent
Explanation
A binomial distribution requires that every trial performed has an outcome independent of previous ones. The occurrence of a success in one trial does not alter the probability in subsequent trials. This independence assumption is a fundamental prerequisite for applying the binomial probability formula. The binomial distribution models the number of successes in a fixed number of binary trials. Each individual trial in this sequence results in either a designated success or failure. The probability of success must remain strictly constant across every single trial conducted.
Quality control inspectors use binomial models to evaluate defective items sampled with replacement. Medical researchers apply binomial trials to analyze patient response rates to specific treatments. Failing to ensure trial independence leads to severe errors in probability estimation and forecasting. Dependent trials violate the core mathematical assumptions required for standard binomial distribution models. Equally likely describes outcomes within a single sample space rather than consecutive experimental trials. Mutually exclusive events cannot occur simultaneously, which is different from trial outcome independence.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
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