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Fall 2000

# Fall 2000 - STAT-230 FINAL EXAMINATION FALL 2000 1 Stat-230...

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STAT-230 FINAL EXAMINATION FALL 2000 1. Stat-230 has six sections in Fall 2000. Five friends take this course and each of them chooses a section at random. (a) [4] Calculate the probability that they are all in the same section. (b) [4] Calculate the probability that they are all in different sections. (c) [4] Calculate the probability that two of them are in one section, and the other three are in other three different sections. 2. A box contains 6 red balls and 9 blue balls. All balls are distinguishable. Let X = the number of red balls among 10 randomly selected balls from the box; Y = the total number of balls selected from the box to get the first red ball. (a) [4] Suppose balls are selected with replacement, give expressions for (i) the probability function of X . (ii) the probability function of Y . (b) [4] Suppose balls are selected without replacement, give expressions for (i) the probability function of X . (ii) the probability function of Y . (c) [4] Suppose 5 yellow balls are added to the box, so the box contains 6 red, 9 blue and 5 yellow balls. Twelve balls are selected at random from the box with replacement , let X 1 , X 2 and X 3 be the number of red, blue and yellow balls selected, respectively.

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Fall 2000 - STAT-230 FINAL EXAMINATION FALL 2000 1 Stat-230...

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