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Winter 2001

# Winter 2001 - STAT 230 FINAL EXAM WINTER 2001 1 A group of...

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STAT 230 FINAL EXAM WINTER 2001 1. A group of 60 Waterloo students consists of 10 Stats, 30 CS, and 20 AM students. (a) How many distinct ways can these students be ordered in a row if we do not distinguish between students in the same degree program? (b) If the students are ordered at random, find the probability that the Statistics students are split with 5 at each end of the row. (c) If 5 students are selected at random (without replacement) give an exact expression for the probability that 3 are CS students. (d) Give an appropriate approximation to the probability in (c) and evaluate it numerically. 2. A die is loaded to give the following probabilities number 1 2 3 4 5 6 probability .3 .1 .15 .15 .15 .15 The die is rolled (independently) 4 times. Find the probability that (a) 2 does not occur (b) neither 2 nor 5 occurs (c) both 2 and 5 occur (d) 2 occurs but 5 does not 3. Five identical bowls are labelled 1,2,3,4, and 5. Bowl i contains i white and 5 - i black balls, i = 1 , 2 , . . . , 5. A bowl is randomly selected and two balls are randomly chosen (without replacement) from the contents of the bowl.

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Winter 2001 - STAT 230 FINAL EXAM WINTER 2001 1 A group of...

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