sample_partial2012 - Probability Theory(107BX Midcourse Exam Solutions 1 Suppose that in a group of 20 students 10 students are Dutch 6 students are

# sample_partial2012 - Probability Theory(107BX Midcourse...

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Probability Theory (107BX)Midcourse ExamSolutions1.Suppose that in a group of 20 students, 10 students are Dutch, 6 students are German,and 4 students are Belgian. Two students are selected at random.(a)What is the sample space?(b)How many ways are there to select two students such that they are both Dutch?Have the same nationality?(c)What is the probability that the two students selected are both Dutch? Have thesame nationality?Solution:
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2.Suppose that for a market survey you send out questionaires toN= 1200 persons. Eachrecipient responds independently with probabilityθ= 0.8. LetXbe the total numberof respondents.(a)What is the distribution ofX?(b)Suppose you want at least 1000 responses for your analysis.Find an expressionfor the probability that you receive less than 1000 responses. You do not need tocalculate this probability.(c)Give an approximate value for the probability that you receive less than 1000 re-sponses.Solution: