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On Halloween night, while trick-or-treating, Lucy is offered a bowl that contains only lemon candies and chocolate bars. If Lucy randomly takes 5 items from the bowl without replacement, what is the probability that at least n of the 5 items are lemon candies?
(1) The probability that all 5 items Lucy takes are chocolate bars is \(\frac{1}{21}\).
(2) \(n = 1\).
(1) The probability that all 5 items Lucy takes are chocolate bars is \(\frac{1}{21}\).
(2) \(n = 1\).
26 Apr 2026, 14:34
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Official Solution:
On Halloween night, while trick or treating, Lucy is offered a bowl that contains only lemon candies and chocolate bars. If Lucy randomly takes 5 items from the bowl without replacement, what is the probability that at least \(n\) of the 5 items are lemon candies?
(1) The probability that all 5 items Lucy takes are chocolate bars is \(\frac{1}{21}\).
This statement gives only the probability that Lucy gets 0 lemon candies, all 5 items are chocolate bars. The question, however, asks for the probability that Lucy gets at least \(n\) lemon candies, and \(n\) is unknown. Not sufficient.
(2) \(n = 1\).
This statement tells us that \(n = 1\), so the question becomes: what is the probability that Lucy gets at least 1 lemon candy? But we still do not know how many candies of each kind are in the bowl. Not sufficient.
(1)+(2) With \(n = 1\), we want \(P(\text{at least 1 lemon}) = 1 - P(\text{0 lemons})\), and (1) gives \(P(\text{0 lemons}) = \frac{1}{21}\), so the required probability is \(1 - \frac{1}{21} = \frac{20}{21}\). Sufficient.
Answer: C
On Halloween night, while trick or treating, Lucy is offered a bowl that contains only lemon candies and chocolate bars. If Lucy randomly takes 5 items from the bowl without replacement, what is the probability that at least \(n\) of the 5 items are lemon candies?
(1) The probability that all 5 items Lucy takes are chocolate bars is \(\frac{1}{21}\).
This statement gives only the probability that Lucy gets 0 lemon candies, all 5 items are chocolate bars. The question, however, asks for the probability that Lucy gets at least \(n\) lemon candies, and \(n\) is unknown. Not sufficient.
(2) \(n = 1\).
This statement tells us that \(n = 1\), so the question becomes: what is the probability that Lucy gets at least 1 lemon candy? But we still do not know how many candies of each kind are in the bowl. Not sufficient.
(1)+(2) With \(n = 1\), we want \(P(\text{at least 1 lemon}) = 1 - P(\text{0 lemons})\), and (1) gives \(P(\text{0 lemons}) = \frac{1}{21}\), so the required probability is \(1 - \frac{1}{21} = \frac{20}{21}\). Sufficient.
Answer: C
