ง C Q. No.4. (a) An urn contains 10 white and 3 black balls. Another urn contains 3 white and 5 black balls. Two balls are transferred from first urn and placed in the second and then one ball is taken from the latter. What is the probability that it is a white ball? (b) Differentiate between Poisson distribution and Poisson process. Give examples in each case.

The number of typing errors made by a typist has a Poisson distribution with an average of three and a half errors per page. If five or more errors appear on a given page, the typist must retype the whole page.    What is the probability that the typist makes 3 errors on a page?  What is the probability that a randomly selected page does not need to be retyped?

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Power failures occur at an electric plant on average 3 times per year. If we can assume this follows a Poisson distribution, answer the following questions. a. What is the probability that there are 4 power failures in 2021? b. What is the probability that there are no more than 2 power failures in a given year? c. How likely is it that there are at least 3 power failures next year?