1. If 8 identical blackboards are to be divided among 4 schools, how many divisi

Question

1. If 8 identical blackboards are to be divided among 4 schools, how many division are possible? How many if each school must receive at least 1 blackboard?

2. A hospital administrator codes incoming patients suffering gunshot wounds according to whether they have insurance (coding 1 if they do and 0 if they do not) and according to their condition, which is rated as good (g), fair (f), or serious (s). Consider an experiment that consists of the coding of such a patient. (a) Give the sample space of this experiment. (b) Let A be the event that the patient is in serious condition. Specify the outcomes in A. (c) Let B be the event that the patient is uninsured. Specify the outcomes in B. (d) Give all the outcomes in the event BC A.

3. Consider 3 urns. Urn A contains 2 white and 4 red balls; urn B contains 8 white and 4 red balls and urn C contains 1 white and 3 red balls. If 1 ball is selected from each urn, what is the probability that the ball chosen from urn A was white, given that exactly 2 white balls were selected?

4. A total of 48 percent of the women and 37 percent of the men that took a certain “quit smoking” class remained nonsmokers for at least one year after completing the class. These people then attended a success party at the end of a year. If 62 percent of the original class was male, (a) what percentage of those attending the party were women? (b) what percentage of the original class attended the party?

5. There are 3 coins in a box. One is a two-headed coin, another is a fair coin, and the third is a biased coin that comes up heads 75 percent of the time. When one of the 3 coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin?

Explanation / Answer

1)

Let the schools be S1, S2,S3,S4

S1+S2+S3+S4 = 8

There are ((n1 C r1) distinct positive integer-valued vectors (x1,x2,...,xr))satisfying the equation

x1+x2+...+xr=n, xi>0,i=1,...,r

So answer is (8-1 C4-1) = 7C3 = 35

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