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Home » Total outcomes: $101^3 = 1030301$ - DNSFLEX

Total outcomes: $101^3 = 1030301$ - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 \boxed{30^\circ}, \boxed{90^\circ}, \boxed{150^\circ}

📌 $$Question: A science educator is designing a probability-based game for elementary students using a fair 10-sided die (numbered 1 through 10). If a student rolls the die four times, what is the probability that exactly two of the rolls result in a number greater than 7?

📌 To solve this, we use the **binomial probability formula**, since each die roll is independent, and we're interested in a specific number of successes (rolling a number greater than 7) in a fixed number of trials (4 rolls).

📌 Numbers greater than 7 on a 10-sided die: 8, 9, 10 → 3 outcomes

📌 Probability of success (rolling >7): $ p = \frac{3}{10} = 0.3 $

📌 Probability of failure (rolling ≤7): $ 1 - p = 0.7 $

📌 Number of trials $ n = 4 $

📌 Number of successes desired $ k = 2 $

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