I LOVE TO EAT DUCKS!!

Algebra Level pending

Two ducks, Wat and Q, are taking a math test with 1022 other ducklings. The test has 30 questions, and the nth question is worth n points. The ducks work independently on the test. Wat gets the nth problem correct with probability 1/ n2 while Q gets the nth problem correct with probability 1/ n+1 . Unfortunately, the remaining ducklings each answer all 30 questions incorrectly. Just before turning in their test, the ducks and ducklings decide to share answers! On any question which Wat and Q have the same answer, the ducklings change their answers to agree with them. After this process, what is the expected value of the sum of all 1024 scores?


The answer is 1020.

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