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how long is term for a senator - Decision Point

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Question: A philosopher of science is analyzing 12 key scientific theories, 5 of which were proposed in the 20th century. If she randomly selects 4 for comparative historical analysis, what is the probability that exactly 2 of them are from the 20th century?

📌 We use combinations to find the probability.

📌 Total number of ways to choose 4 theories from 12:

📌 \binom{12}{4} = 495

📌 Number of favorable outcomes (choosing 2 from the 5 20th-century theories and 2 from the 7 others):

📌 \binom{5}{2} \cdot \binom{7}{2} = 10 \cdot 21 = 210

📌 \frac{210}{495} = \frac{14}{33}

📌 \boxed{\frac{14}{33}}

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