#### 539.39

February 22, 2026

#### 539.39

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Day 4: 80 × (1.15)^3 = <<80*1.15^3=121.67>>121.67
Day 5: 80 × (1.15)^4 = <<80*1.15^4=139.9205>>139.9205
Sum: 80 + 92 + 105.8 + 121.67 + 139.9205 = <<80+92+105.8+121.67+139.9205=539.3905>>539.3905
A philosopher of science examines 8 scientific paradigms. If each paradigm has a 70% chance of being overturned in a paradigm shift, and their fates are independent, what is the probability that exactly 5 paradigms are overturned?
This is a binomial probability: P(k=5) = C(8,5) × (0.7)^5 × (0.3)^3.
C(8,5) = C(8,3) = (8×7×6)/(3×2×1) = <<(8*7*6)/(3*2*1)=56>>56.

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