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Total width of icons: \( 12 \times 60 = 720 \) px - GetMeFoodie

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 5Question: An entomologist is studying the pollination habits of a certain species of bee that visits 5 different flowers in a garden. If each bee chooses its next flower uniformly at random from the remaining unvisited flowers, what is the probability that the bee visits flower A before flower B and flower B before flower C, in some sequence among the 5 flowers?

📌 Solution: We are given that a bee visits 5 flowers in random order, and we are to compute the probability that flowers A, B, and C are visited in increasing order (i.e., A before B, B before C), not necessarily consecutively. The bee chooses its next flower uniformly at random from unvisited ones. Since all permutations of the 5 flowers are equally likely (due to the uniform random selection assuming no memory bias), we consider all $5!$ permutations of the flowers.

📌 We are interested in the conditional ordering of A, B, and C within the sequence. Among all permutations, the relative order of A, B, and C (ignoring the others) can be any of the $3! = 6$ possible orderings. Since the bee visits flowers randomly and no preference is indicated, each of these 6 orderings is equally likely.

📌 We want the specific order: A before B before C. Only one of the six possible relative orderings satisfies this.

📌 Question: A pharmacologist is testing combinations of 3 distinct experimental compounds selected from a pool of 10 promising drug candidates. If the efficacy of the trio depends critically on one specific compound being included (say, Compound X), what is the probability that Compound X is among the 3 chosen, given that at least one of the two most powerful compounds (A or B) is included?

📌 First, compute $ P(F) $: the probability that at least one of A or B is in the trio.

📌 Thus, the number of 3-element subsets containing X and at least one of A or B is:

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