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Unformatted text preview: Lecture 4. Examples Problem 1.1. A ship is carrying r Russians and g Georgians and no one else. A committee of k people is to be selected randomly to assume the task of rationing the rum. What is the probability that there will be x Russians on the rum committee? Solution. The sample space (set of all outcomes) is the set of all committees. There are ( r + g k ) elements, each equally likely. We must count the number of committees with x Russians. There are ( r x ) ways to pick the Russians, but then we must also pick n- k Georgians, and there are ( g k- x ) way to do this. Thus, there are ( r x ) ( g k- x ) ways to make a committee with x Russians, so the desired probability is: ( r x ) ( g k- x ) ( r + g k ) . Problem 1.2. The last problem in Lecture 3 had ( r k ) + ( g k ) ( r + g k ) as its answer. Why do both problems have the same denominator? Why does one problem have addition in the numerator, while the other has multiplication? Problem 1.3. At a tea party, a lady claimed to be able to tell by taste alone whether, in a cup of tea with milk, the tea or the milk had been poured first. The famous statistician R.A.Fisher was present, and he proposed presenting the lady with 8 cups, four of each kind, in random order and asking her to classify them. She was told that there were fourkind, in random order and asking her to classify them....
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This note was uploaded on 11/29/2011 for the course MATH 3355 taught by Professor Britt during the Spring '08 term at LSU.
- Spring '08