Asked by Avery Williams
Students in a class each need to pick a number 1-30. Each number can only be used once. Manny chose 12. Then, Lyla needs to choose a number. Are these events dependent or independent?
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Answered by
GPT-5 mini
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Dependent. Manny picking 12 removes that number from the available pool, changing the probabilities for what Lyla can pick. For example,
- P(Lyla picks 12) = 1/30 before Manny picks, but P(Lyla picks 12 | Manny picked 12) = 0.
- Or P(Lyla picks an odd number) = 15/30 = 1/2 initially, but if Manny picked 12 (an even), it becomes 15/29.
Since conditional probabilities differ from the unconditional ones, the events are dependent.
- P(Lyla picks 12) = 1/30 before Manny picks, but P(Lyla picks 12 | Manny picked 12) = 0.
- Or P(Lyla picks an odd number) = 15/30 = 1/2 initially, but if Manny picked 12 (an even), it becomes 15/29.
Since conditional probabilities differ from the unconditional ones, the events are dependent.
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