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left and right hand - Imagemakers

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 Question: A postdoctoral researcher is analyzing data from 7 experimental trials. If 3 trials are randomly selected for peer review, what is the probability that a specific trial of particular interest is among those selected?

📌 Solution: The total number of ways to choose 3 trials from 7 is:

📌 To ensure the specific trial is included, we fix it and choose 2 more from the remaining 6:

📌 Thus, the probability that the specific trial is selected is:

📌 Question: A chemical engineer is analyzing 10 different temperature settings for a reactor. If 5 settings are randomly chosen for calibration, what is the probability that a critical temperature (known to be among the 10) is included?

📌 Solution: The total number of ways to choose 5 settings from 10 is:

📌 To count the favorable outcomes where the critical temperature is included, we fix that temperature and choose the remaining 4 from the other 9:

📌 The probability that the critical temperature is among the selected 5 is:

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