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Number of successful attempts of crossword puzzles

Number of successful attempts of crossword puzzles

IB Year 5 | Grade 11

A crossword puzzle is published in ‘The Times’ each day of the week, except Sunday. A man can complete, on average, \(8\) out of \(10\) of the crossword puzzles.

  1. Find the expected value and the standard deviation of the number of completed crosswords in a given week.
  2. Find the probability that he will complete at least \(5\) in a given week.
  3. Given that he completes the puzzle on Monday, find the probability that he will complete at least \(4\) in the rest of the week.
  4. Find the probability that, in a period of four weeks, he completes \(4\) or less in only one of the four weeks.

Solution:

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Answer:Under the stated independent-outcome model: (a) Mean \(4.8\), SD \(0.980\) crosswords. (b) \(0.655\). (c) \(0.737\). (d) \(0.388\). Probabilities and SD to 3 s.f.

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