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📰 5Question: A cognitive scientist is analyzing decision-making strategies in which participants choose between four equally likely options. If a participant selects one option at random each time and makes exactly four independent choices, what is the probability that exactly two of the chosen options are the same and the other two are each different from each other and from the repeated one? 📰 We are to compute the probability that in 4 independent choices among 4 options (say labeled A, B, C, D, with equal likelihood), exactly one option appears twice, and two other distinct options appear once each, with the fourth position filled by a fourth distinct option — but wait: this would require 4 distinct options total, and one repeated. Since only 4 positions exist, and we want exactly one option repeated, and the other two being different, the only valid pattern is: one option appears twice, two others appear once, and the fourth option appears zero times — but that’s only 4 choices total. So the pattern is: one option repeated twice, and two other distinct options appearing once each — that uses up 2 + 1 + 1 = 4 choices, with one option appearing twice and two others once each, and one option not used at all. So the multiset of choices is of the form {A, A, B, C}, where A, B, C are distinct, and D is unused. 📰 We compute the probability of such a multiplicity pattern. 📰 Sanditon Season 3 1676534 📰 Gallaudet University 3753155 📰 Cenotes Mexico Hidden Treasures Few Know About 8479526 📰 Dagne Dover 3389206 📰 Best Cord Cutting Options 7233459 📰 Best Free Website Builder 6424458 📰 Having By In Sql 4380343 📰 Skate 3 Steam 2849812 📰 5Navigating Through Design How Construction Graphics Shapes Mandalays Urban Identity 8311769 📰 No More Leakssee The Breathtaking Secret Behind Perfect Pond Liners 1621959 📰 The River Is Waiting The Silent Warning Hidden In Its Gently Curving Flow Only The Brave Will Hear 6360051 📰 Plum Blossom Meaning 8823585 📰 Unleash Hidden Crazy Tetris Gamesno One Was Ready For This Level Of Tetris Madness 9480578 📰 Life Insurance Policy Cost 8286131 📰 61 A Car Travels 150 Miles In 25 Hours If It Continues At The Same Speed How Far Will It Travel In 7 Hours 6994992