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Home » \( a_10 = S_10 - S_9 = 350 - 288 = 62 \) - High Altitude Science

\( a_10 = S_10 - S_9 = 350 - 288 = 62 \) - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 A philosopher of science studying the nature of scientific knowledge considers a logical sequence of hypotheses: Suppose a researcher forms hypotheses such that each new hypothesis is supported by two independent pieces of evidence, each of which increases the credibility of the hypothesis by 25%. If the initial credibility is 40%, what is the credibility after adding 4 such independent pieces of evidence?

📌 Let the initial credibility be \(C_0 = 40\% = 0.4\).

📌 Each piece of independent evidence increases credibility by 25% of the **current** credibility. This is multiplicative: each new evidence multiplies credibility by \(1.25\).

📌 After 4 independent pieces, the credibility is:

📌 C = 0.4 \times (1.25)^4

📌 1.25^4 = (1.25^2)^2 = 1.5625^2 = 2.44140625

📌 C = 0.4 \times 2.44140625 = 0.9765625

📌 C = 97.65625\%

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