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what does a real id look like in indiana - IQnection

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 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.

📌 Product: 56 × 0.16807 × 0.027 = 56 × 0.00453789 = <<56*0.00453789=0.25412184>>0.2541 (rounded to four decimals).

📌 #### 0.2541

📌 An entomologist tracks a bee colony that starts with 12,000 bees. Each day, 4% of the bees die, but 800 new bees are born. What is the bee population after 3 days?

📌 Day 1: Start with 12,000. After 4% die: 12,000 × 0.96 = <<12000*0.96=11520>>11,520. Add 800: 11,520 + 800 = <<11520+800=12320>>12,320.

📌 Day 2: 12,320 × 0.96 = <<12320*0.96=11827.2>>11,827.2 → add 800: 11,827.2 + 800 = <<11827.2+800=12627.2>>12,627.2.

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