Probability using Poisson Distribution

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The discussion revolves around calculating probabilities using the Poisson distribution for typographical errors in a book. The problem involves finding the probability of a page containing no errors and at least three errors, given that there are 600 errors in a 600-page book. The mean number of errors per page, λ, is determined to be 1. The correct calculation for the probability of no errors on a page yields approximately 0.37, aligning with the expected result. The conversation highlights the importance of correctly applying the Poisson formula for accurate probability outcomes.
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Homework Statement



Suppose a typographical errors committed by a typesetter occurs randomly. If that a book of 600 pages contains 600 such errors, calculate the probability by using Poisson's distribution.
i) that a page contains no errors
ii) that a page contains at least three errors


Homework Equations



W(n) = \lambdan e -\lambda / n!

The Attempt at a Solution



I related \lambda = Np, the mean number of errors and proceeded. I am supposed to get 0.37 for part i) of the problem but I didn't get it right. Any suggestion?


Berkeley
 
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Isn't lambda the mean number of errors per page? If so, it would be 1. Using the formula, W(0) = 1^0 * e^(-1)/0! = 1/e ~ .37
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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