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314 207 in expanded form - Parker Core Knowledge

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 A home-schooled STEM student is studying probability with a jar containing 5 red candies, 4 blue candies, and 3 yellow candies. If the student draws three candies at random without replacement, what is the probability that exactly one candy of each color is drawn?

📌 Favorable outcomes: one red, one blue, one yellow:

📌 A space agriculture designer is programming a robotic arms system to tend three identical hydroponic beds on a Mars habitat. The arms operate independently and each randomly selects a bed to service every hour. What is the probability that after three hours, each bed has been serviced at least once?

📌 Each hour, one of 3 beds is chosen uniformly at random. We want the probability that all 3 beds are serviced at least once in 3 hours.

📌 This is equivalent to counting the number of sequences of length 3 using 3 symbols (beds) where all symbols appear at least once. Since the length is exactly 3 and we need all 3 beds, this occurs only when all choices are distinct.

📌 A digital engagement strategist analyzes user interaction times on a nonprofits virtual tour platform. If three users independently spend a whole number of minutes (between 1 and 50 inclusive) engaging with the platform, what is the probability that the total engagement time is exactly 100 minutes?

📌 We seek the number of integer solutions to:

📌 A home-schooled student is experimenting with dice in a probability lab. They roll a fair 6-sided die four times. What is the probability that exactly two of the rolls show a prime number?

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