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06 Aug 2026, 10:53
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At a volunteer orientation, 8 participants are in a training group. If three participants are randomly selected without replacement, what is the probability that all three selected participants have prior volunteer experience?
(1) If two participants are randomly selected from the group without replacement, the probability that neither participant has prior volunteer experience is greater than \(0.5\).
(2) If one participant is randomly selected from the group, the probability that the participant has prior volunteer experience is less than \(0.3\).
(1) If two participants are randomly selected from the group without replacement, the probability that neither participant has prior volunteer experience is greater than \(0.5\).
(2) If one participant is randomly selected from the group, the probability that the participant has prior volunteer experience is less than \(0.3\).
06 Aug 2026, 10:53
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Official Solution:
At a volunteer orientation, 8 participants are in a training group. If three participants are randomly selected without replacement, what is the probability that all three selected participants have prior volunteer experience?
(1) If two participants are randomly selected from the group without replacement, the probability that neither participant has prior volunteer experience is greater than \(0.5\).
Let’s check whether there can even be 3 participants with prior volunteer experience.
If 3 participants had prior volunteer experience, then 5 participants would have no prior volunteer experience. In that case, the probability that 2 selected participants both have no prior volunteer experience would be:
\(\frac{5}{8} * \frac{4}{7} = \frac{5}{14}\), which is less than \(0.5\).
So, there must be more than 5 participants who have no prior volunteer experience, and therefore fewer than 3 participants who have prior volunteer experience. Therefore, the probability that all 3 selected participants have prior volunteer experience is 0.
Sufficient.
(2) If one participant is randomly selected from the group, the probability that the participant has prior volunteer experience is less than \(0.3\).
This implies that there must be fewer than:
\(0.3 * 8 = 2.4\)
participants with prior volunteer experience. Since the number of participants must be an integer, at most 2 participants have prior volunteer experience. Therefore, the probability that all 3 selected participants have prior volunteer experience is 0.
Sufficient.
Answer: D
At a volunteer orientation, 8 participants are in a training group. If three participants are randomly selected without replacement, what is the probability that all three selected participants have prior volunteer experience?
(1) If two participants are randomly selected from the group without replacement, the probability that neither participant has prior volunteer experience is greater than \(0.5\).
Let’s check whether there can even be 3 participants with prior volunteer experience.
If 3 participants had prior volunteer experience, then 5 participants would have no prior volunteer experience. In that case, the probability that 2 selected participants both have no prior volunteer experience would be:
\(\frac{5}{8} * \frac{4}{7} = \frac{5}{14}\), which is less than \(0.5\).
So, there must be more than 5 participants who have no prior volunteer experience, and therefore fewer than 3 participants who have prior volunteer experience. Therefore, the probability that all 3 selected participants have prior volunteer experience is 0.
Sufficient.
(2) If one participant is randomly selected from the group, the probability that the participant has prior volunteer experience is less than \(0.3\).
This implies that there must be fewer than:
\(0.3 * 8 = 2.4\)
participants with prior volunteer experience. Since the number of participants must be an integer, at most 2 participants have prior volunteer experience. Therefore, the probability that all 3 selected participants have prior volunteer experience is 0.
Sufficient.
Answer: D
