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Home » First, calculate the semi-perimeter \( s \) of the triangle: - ClickBalance

First, calculate the semi-perimeter \( s \) of the triangle: - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 \binom{7}{2} \times \binom{9}{2} = \left(\frac{7 \times 6}{2 \times 1}\right) \times \left(\frac{9 \times 8}{2 \times 1}\right) = 21 \times 36 = 756

📌 Therefore, the probability is:

📌 \frac{756}{1820} = \frac{189}{455}

📌 So, the probability of drawing exactly two red marbles is $\boxed{\dfrac{189}{455}}$

📌 Question: If I roll a fair six-sided die four times, what is the probability that I roll the number 4 exactly twice?

📌 Solution: This is a binomial probability problem with $ n = 4 $ trials (rolls), success probability $ p = \frac{1}{6} $ (rolling a 4), and we want exactly $ k = 2 $ successes.

📌 The binomial probability formula is:

📌 P(k) = \binom{n}{k} p^k (1-p)^{n-k}

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