* KINDLY REPLY THE ANSWER USING EXCEL WORKSHEET AND ALSO USING FORMULA TO DERIVE THE ANSWER. EACH PROBLEM TO A DEDICATED WORKSHEET.
Problem 1
An urn contains 40 balls, of which 18 are red and the other 22 blue. Suppose you take out 12 balls from this urn, without replacement. What is the probability that exactly 5 are red and 7 are blue among the 12 balls you choose?
Problem 2
Ten chairs in a row are to be occupied by seven students and Professors Alpha, Beta, and Gamma. These three professors arrive before the seven students and decide to choose their chairs so that each professor will be between two students. In how many ways can Professors Alpha, Beta, and Gamma choose their chairs?
Problem 3
Eight people get into an elevator at the ground floor of a hotel which has 11 upper floors. Assuming each person gets off at a randomly chosen floor, what is the probability that no two people get off at the same floor?
Problem 4
A random variable X is binomially distributed with mean 6 and variance 4.2. What is P(X ≤ 5)?
Problem 5
Each student is likely to be absent from a class 15% of the time. A class is cancelled if the number of attendants is not more than 11 out ofthe total registered 100. What is the expected numbers present in a class and what is the probability that a class will be canceled?
Problem 6
Answer the following problem from Bertsimas, Dimitris, and Robert Freund. Data, Models, and Decisions: The Fundamentals of Management Science. Charlestown, MA: Dynamic Ideas, 2004. ISBN: 9780975914601.
Chapter 4, p185
Housing Prices in Lexington, Massachusetts
Table 4.7: VALMAX Sales
House 
Asking Price 
Selling Price 
Difference 
Number 
($) 
($) 
($) 
1 
290,000 
275,000 
15,000 
2 
315,000 
314,000 
1,000 
3 
299,000 
310,000 
11,000 
4 
615,000 
610,000 
5,000 
5 
345,000 
345,000 
0 
6 
230,000 
221,000 
9,000 
7 
420,000 
418,000 
2,000 
8 
399,000 
382,000 
17,000 
9 
549,000 
555,000 
6,000 
10 
299,000 
292,000 
7,000 
11 
430,000 
431,000 
1,000 
12 
330,000 
303,000 
27,000 
13 
395,000 
381,000 
14,000 
14 
675,000 
661,000 
14,000 
15 
460,000 
443,000 
17,000 
16 
437,000 
449,000 
12,000 
17 
680,000 
668,000 
12,000 
18 
380,000 
385,000 
5,000 
19 
325,000 
310,000 
15,000 
20 
435,000 
435,000 
0 
21 
304,000 
300,000 
4,000 
22 
552,000 
560,000 
8,000 
23 
403,000 
389,000 
14,000 
24 
419,000 
425,000 
6,000 
25 
227,000 
217,000 
10,000 
26 
340,000 
342,000 
2,000 
27 
619,000 
615,000 
4,000 
28 
312,000 
308,000 
4,000 
29 
320,000 
319,000 
1,000 
30 
299,000 
270,000 
29,000 
31 
289,000 
280,000 
9,000 
32 
316,000 
319,000 
3,000 
33 
328,000 
320,000 
8,000 
34 
610,000 
615,000 
5,000 
35 
350,000 
353,000 
3,000 
Table 4.8: Others Sales
House 
Asking Price 
Selling Price 
Difference 
Number 
($) 
($) 
($) 
1 
295,000 
280,000 
15,000 
2 
425,000 
411,000 
14,000 
3 
299,000 
285,000 
14,000 
4 
299,000 
299,000 
0 
5 
475,000 
471,000 
4,000 
6 
350,000 
348,000 
2,000 
7 
429,000 
418,000 
11,000 
8 
399,000 
401,000 
2,000 
9 
489,000 
476,000 
13,000 
10 
299,000 
270,000 
29,000 
11 
539,000 
531,000 
8,000 
12 
225,000 
214,000 
11,000 
13 
749,000 
735,000 
14,000 
14 
689,000 
664,000 
25,000 
15 
469,000 
476,000 
7,000 
16 
299,000 
270,000 
29,000 
17 
539,000 
531,000 
8,000 
18 
199,000 
205,000 
6,000 
19 
349,000 
335,000 
14,000 
20 
689,000 
687,000 
2,000 
21 
485,000 
479,000 
6,000 
22 
299,000 
285,000 
14,000 
23 
305,000 
275,000 
30,000 
24 
479,000 
469,000 
10,000 
25 
699,000 
677,000 
22,000 
26 
339,000 
325,000 
14,000 
27 
195,000 
209,000 
14,000 
28 
539,000 
535,000 
4,000 
29 
279,000 
268,000 
11,000 
30 
459,000 
469,000 
10,000 
31 
679,000 
659,000 
20,000 
32 
729,000 
725,000 
4,000 
33 
215,000 
214,000 
1,000 
34 
539,000 
525,000 
14,000 
35 
289,000 
270,000 
19,000 
36 
479,000 
469,000 
10,000 
37 
389,000 
390,000 
1,000 
38 
419,000 
410,000 
9,000 
39 
339,000 
339,000 
0 
40 
469,000 
462,000 
7,000 
41 
299,000 
280,000 
19,000 
42 
289,000 
280,000 
9,000 
43 
419,000 
403,000 
16,000 
44 
289,000 
275,000 
14,000

Subject  Mathematics 
Due By (Pacific Time)  07/23/2015 12:00 am 
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