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calzone vs stromboli - IQnection

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 \text{Total paths} = \binom{7}{4} = 35

📌 Now, fix the first move as F and the last move as R.

📌 That leaves us with: 3 F’s and 2 R’s to arrange in the middle 5 positions.

📌 Number of such favorable paths:

📌 \binom{5}{3} = 10

📌 \frac{10}{35} = \frac{2}{7}

📌 Hence, the probability is $ \boxed{\frac{2}{7}} $.

📌 Question: A data scientist trains a model using sequences of 5 binary features, each being 0 or 1. If each feature is independently set to 1 with probability $ \frac{1}{3} $, what is the probability that exactly 3 of the 5 features are 1?

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