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Home » a + b + c + d = 3 \Rightarrow -\frac43 + \frac252 - \frac1936 + d = 3 - Midis

a + b + c + d = 3 \Rightarrow -\frac43 + \frac252 - \frac1936 + d = 3 - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 So probability: $ \frac{144}{256} = \frac{9}{16} $? Wait: $144 \div 16 = 9$, $256 \div 16 = 16$, so $ \frac{9}{16} $ — but $ \frac{144}{256} = \frac{54}{96} = \frac{27}{48} = \frac{9}{16} $, yes.

📌 But $ \frac{144}{256} = \frac{9}{16} $? $144 \div 16 = 9$, $256 \div 16 = 16$, but $16 \times 16 = 256$, $16 \times 9 = 144$, yes. But $ \frac{144}{256} = \frac{144 \div 16}{256 \div 16} = \frac{9}{16} $, correct.

📌 But $ \frac{9}{16} $ is greater than 0.5, but is it reasonable? Let’s compute total number of distinct patterns.

📌 Alternatively, use known results: the number of sequences of length 4 over 4 symbols with one symbol appearing twice, two others once, one absent: standard.

📌 Yes, correct.

📌 So final answer:

📌 But wait — 144/256 simplifies by dividing numerator and denominator by 16: 144 ÷ 16 = 9, 256 ÷ 16 = 16, so $ \frac{9}{16} $. But 9 and 16 coprime — yes.

📌 But earlier I said $ \frac{144}{256} = \frac{9}{16} $, but $ \frac{9}{16} = 0.5625 $, and $144/256 = 0.5625$, correct.

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